You grasp the sheer scale of London's wealth when you look down at it from the sky.
Skyscrapers tower above the City and Docklands like vast monuments to finance.
Shoppers teem around Oxford Street and Piccadilly. Georgian terraces and inter-war suburbs alike are not just homes but also prime real estate.
And with wealth comes power. London is a global city whose dominant status both within the UK and the rest of the world is unquestionable.
For some British people, all this is a cause for pride and celebration. For others it's a source of resentment and unease.
How did it get to this position?
London's stature is remarkable. Can anywhere else claim to be both an international focal point of such significance and so commanding a national capital?
Just before this year's UK General Election, listeners of US National Public Radio were told that it “completely dominates the political, cultural and economic life of the UK to an extent rarely seen elsewhere”.
New York might rival it as an economic hub – though London recently overtook its US rival in the Global Financial Centres Index (GFCI) rankings. But New York isn't at the same time the seat of political power in the US or home to the nation's central bureaucracy.
Paris dominates France, but lags behind its British counterpart in terms of international finance, sitting at 37th in the GFCI table.
No-one doubts London's pervasive economic influence. More than a third of global foreign exchange takes place every day in London.
The city is home to 251 overseas banks. UK financial services had a trade surplus of $71bn in 2013. London's GDP is equal to that of Saudi Arabia.
And in relation to the rest of the UK, London's dominance is especially striking.
The capital generates 22% of UK GDP despite accounting for only 12.5% of the UK population. According to the Centre for Economic and Business Research, it makes a net contribution to the Exchequer of an astonishing £34bn.
Inner London's GDP per head was 328% of the European Union average in 2010, compared with 70% in west Wales - the biggest gap in any EU state, said the European Commission's statistics agency Eurostat. Among the next eight largest UK cities, only one other, Bristol, has a GDP that is above the national average.
In 2013 it was estimated that in property terms London's top 10 boroughs were worth more than all of Northern Ireland, Scotland and Wales combined. London's housing stock is worth as much as Brazil's annual GDP, estate agents Savills reported in January 2015.
A cul-de-sac comprising a score of 1930s semi-detached homes in Ilford or Hounslow might easily be worth £10m.
Not that all Londoners are enjoying this prosperity.
A 2013 report by the New Policy Institute suggested that 28% of people in London were in poverty, seven percentage points higher than the remainder of England. Two of the city's boroughs are among England's top 10 most deprived. If the capital is a place where wealth is concentrated it is also one where inequality is highly visible and inescapable.
But just as London's wealth is not shared by all who live there, the city's dominance is not just about economic performance. The UK's parliament is in London. So too is Whitehall's central government machinery - London had 76,840 civil servants in 2014.
The default position is that major businesses and institutions, from Shell to the British Museum - not to mention the BBC - are headquartered in the capital as a matter of course.
London is Europe's fastest-growing technology cluster, with 3,000 companies concentrated in the East End. The British film industry is synonymous with the names of places in and around London - Ealing, Pinewood, Shepperton. The city is a major international centre for fashion, art and theatre, too.
“It's where all the rich people are,” says John Lanchester, author of Capital and How to Speak Money. “It's where all the media is, all the power is, all the culture is, all the money is - that is a lot of alls. Around the country people look at London and they don't really recognise themselves.”
Compare this with Germany, where the political capital Berlin is balanced by a financial hub in Frankfurt and powerful industrial and media centres in Munich and Hamburg. New York's global status doesn't diminish Washington's political clout, Los Angeles' entertainment output or San Francisco's position at the vanguard of the technology industry.
Taking into account population size relative to the rest of the country, only Moscow among major global capitals accounts for a greater share of national product, wrote Danny Dorling, professor of geography at the University of Oxford. Even Paris takes a lower share of French GDP.
And despite devolution, and the efforts of organisations like the BBC and the civil service to shift jobs into the regions, London enjoys a status within the UK that no other British city can compete with, and a reputation for being a worldwide cultural centre - particularly in relation to youth culture.
And so it attracts not just capital but incomers, enticed despite the high cost of living by the prospect of employment and, above all, a desire to be where they perceive the action to be.
For many, London's dominance is a mark of success, not failure, and something to be celebrated.
During his 2014 Conservative party conference speech, the city's mayor, Boris Johnson, hit out at “London-bashing”, arguing that the capital's strong performance was good for the whole country because “when the great London flywheel turns faster and faster it helps to drive the vast and intricately connected locomotive that is the British economy”.
Nonetheless, it's true that London - wealthier, younger, more diverse - thinks and behaves differently from the rest of the UK. In the 2015 election, while Labour fell back elsewhere, it gained seven seats in the capital.
You see it in the way people talk about that much-disparaged young urban tribe, the hipsters.
Take the much-publicised opening of Shoreditch's Cereal Killer Cafe, in which fashionably bearded and tattooed staff sell their clientele bowls of Lucky Charms for £3 a time.
For all the bafflement and outrage this outlet has generated - culminating in it being surrounded by anti-gentrification protesters who threw paint and daubed the word “scum” on its front window - it is emblematic of the “flat white economy” of media, internet and creative businesses said to employ more than 150,000 people in the capital.
In the 24 months to March 2014, 32,000 businesses were created in one modish postcode, EC1V - a triangle between Angel, Clerkenwell and Old Street.
And the contrast between the capital and the provinces is the source of huge and increasingly potent resentments. There are few more powerful insults in British politics than to declare someone a member of the “metropolitan elite” or, for that matter, “London-centric”.
Insurgent movements across the political spectrum, from the Scottish National Party to UKIP, won millions of votes railing against a political class they say ignores the interests and aspirations of those outside the M25.
The names of two London subdivisions - Westminster and the City - are regularly invoked by left and right alike to personify all that is pernicious and corrupt.
A desire to redress the balance is expressed all the way up to the top. In June 2014 the prime minister said that for too long the UK economy had been “too London-focused and too centralised”.
Chancellor George Osborne, launching plans for an economic “northern powerhouse” and devolution for Manchester, said in April the country was “too imbalanced” and “reliant too much on the success of London”.
To judge whether London's success has taken place to the detriment or benefit of the rest of the country it's necessary to look at how it became quite so powerful in the first place.
And to do that one has to start with the waterway flowing through its heart.
On the river
After invading Britain in 43 AD, the Romans settled to the north side of modern St Paul's. They wanted to be close to the river.
“The Thames is the major route with Europe - it's the main way of moving goods and people,” says David Green, professor of geography at Kings College London. “It's tidal and London is at the lowest bridging point.”
London replaced Colchester as the capital of Roman Britain. In the Tudor era, trade flourished and the East India Company was formed. The city's population expanded exponentially, with immigrants flooding in from the rest of Britain, and Huguenot refugees arriving from France.
As the British Empire began its ascendancy, London's location proved ideal. Power was shifting from the Mediterranean to northern Europe, and trade routes were opening up to the New World.
“It's really the 17th Century when you are seeing London beginning to emerge as a global centre,” says Alex Werner, head of history collections at the Museum of London.
While ports like Bristol and Liverpool were growing in importance, London had a major advantage - it was the capital and the centre of government. It quickly became a hub of information, both financial and political.
Social change in England favoured London. England was moving from a feudal nation dominated by the aristocracy to a modern, mercantile democracy.
“London had this large rich, educated middle class,” says Green.
“The crown had never loved London. Monarchs' pursuits were hunting, fishing, shooting. The aristocracy liked to be rural-based. London was a middle-class city. That's why the City of London has this mythical gloss around it.”
Traditionally, the monarch required permission to enter the City of London at Temple Bar.
The industrial revolution saw the rise of cities in the north such as Manchester, Leeds and Liverpool as major industrial centres. Each had their own stock exchanges, their own newspapers. But their challenge to the capital was never sustained.
“By the end of the 19th Century, all this trade had shifted back to London,” says Werner. “You would think a country like Britain could support a variety of centres. But all goes back to London - it's almost magnetic how in a long course of history there are other centres that set themselves up as rivals to London and never quite carry it through.”
While the British Empire was at its peak the predominance of the capital city was unusual even among the major European powers.
Germany and Italy, both of which only achieved complete unification in 1871, still had power diffused among provincial capitals. The seat of government in the Netherlands was The Hague, while Amsterdam was the capital and Rotterdam the largest port. While Paris was arguably Europe's prime cultural centre and at the heart of the centralised French state, geography meant it was never a trading hub to rival London.
And yet London's fortunes had been inextricably linked with England's, and then Great Britain's, place in the world. Two world wars in the first half of the 20th Century would see the British Empire diminished, the UK impoverished and London itself reduced to a bomb-scarred shadow of its imperial glories.
After WW2, London might have been expected to go into a slow and irreversible decline. More than a million homes in the city had been destroyed by bombs in the Blitz. Londoners were leaving in droves for the new towns. The country was virtually bankrupt and the empire was coming to an end.
And yet, once again, London came back.
The Big Bang
Post-war London was an exhausted, run-down, ration-starved place, but it still had plenty going for it. It was located in a convenient time zone, between the working hours of Wall Street and East Asia. Speaking English, the lingua franca of global commerce, helped too.
Throughout the ages, London has displayed an unerring ability to recover from setbacks. “It does well in boom times and less badly in the more difficult times,” says Vanessa Harding, professor of London History at Birkbeck, University of London.
Slowly, London renewed itself.
On the South Bank, the 1951 Festival of Britain presented a vision of a gleaming, futuristic UK. The Clean Air Act finally did away with the smog that had choked the city's air for decades. In 1948 the Empire Windrush brought 492 passengers and one stowaway from Jamaica.
The post-war baby boom, coupled with Londoners enjoying historically high disposable incomes, fuelled demand for pop music and fashion - two commodities for which the city would become famous from the Swinging London era onwards.
A shared language eased access to the huge US market for British rock groups and other cultural exports.
The nascent welfare state and a growing housebuilding programme saw almost 300,000 new properties constructed during the 1960s in the capital, exemplified by developments like the Barbican. This meant would-be artists were able to sustain a bohemian lifestyle relatively cheaply, cementing the city's reputation as a centre for youth culture.
At the same time, London's outlook and infrastructure would allow the city to gradually regain its financial supremacy. Although sterling had lost its pre-eminence as a global currency to the dollar, the City's asset managers were looking abroad to generate returns for their clients, resulting in the growth of the investment management industry.
Financial regulation in New York was far stricter than in London, where the relatively light-touch oversight regime proved attractive to investors. In the post-war period, London became the prime venue for the Eurodollar market - the trading of dollars outside the US. The UK's imperial heritage also meant there was a tradition of drafting international contracts using English contract law.
Despite its temporarily diminished status, London had never quite stopped considering itself the centre of the world.
“You had this very extensive set of historical connections and overseas branches and an international mindset,” says Lanchester. “It was the most mercantile and most open economy in Europe for centuries.”
But most significant of all was the “Big Bang” deregulation of 1986. The sweeping away of the rules and restrictive practices that had once constrained the London stock exchange, as well as the introduction of modern screen-based trading, attracted overseas banks seeking to benefit from a newly liberalised market.
It was this move, more than any other, that secured the city's latter-day financial pre-eminence. London became a financial cluster, in which businesses gained from proximity to each other and to services like accountants and law firms.
This changed London's geography, too. New skyscrapers sprung up. The City - as a financial powerhouse, rather than a geographic entity or administrative unit - extended well beyond the square mile.
Barclays, Citigroup, Credit Suisse First Boston, HSBC and Morgan Stanley decamped east to the reclaimed waste ground of Docklands while the hedge funds set up offices in the Georgian avenues of Mayfair, where they now occupy an estimated 58,000 sq ft of office space.
Supporters said this display of free-market capitalism in action generated huge tax revenues which benefited the UK as a whole.
Before the Big Bang, financial services accounted for 18% of corporate tax receipts. By 2006 they made up 26% - an increase which helped fund increases in public spending. The value of shares traded in London went up by 1,500% over the same period from £161bn to £2,496bn.
But then came the crash of 2007-8, which saw the UK and other major economies plunged into recession. In the UK, at its peak, taxpayers' direct subsidy to banks was £1 trillion, according to the National Audit Office.
Critics blamed, among other factors, an over-reliance on financial services and a lax regulatory regime for prolonging the UK's exposure to the crisis. Last year George Osborne said the British economy remained “unbalanced” and warned that “we cannot put all our chips on the success of the City of London”.
In 2014, financial services were calculated to contribute £126.9bn - with London accounting for more than half of this - to the British economy. Today some 350,000 people in London are still employed in the sector. For better or worse, the UK's fortunes remain inextricably bound up with those of the City.
Searching for fun
The source of London’s power isn’t purely financial. “It's also about where people want to live,” says Werner.
“A lot of businessmen don't like Frankfurt. They much prefer London for its cultural offering.
“If you speak to any teenager in Europe and ask where they want to live they say London. It has this great energy. People from all over the world gravitate here like they do to New York.”
If you can afford it, the city is a congenial place to shop with good schools and plenty to do in the evening. There’s Wimbledon, the Royal Opera House, Premier League football, West End theatre, the Tate Modern. The East End, from Shoreditch to London Fields to Dalston, is arguably the most fashionable urban enclave in Europe.
Five of the world’s best restaurants are in London, according to annual rankings compiled by Restaurant magazine.
To some extent, it is possible to hypothesise a kind of feedback loop operating, whereby the sheer size of London’s population - eight times larger than the next-biggest British city - sustains a better selection of restaurants and bars, which in turn attracts more incomers. Or that its storied legacy of pop music and the theatre attracts ever more aspiring singers and actors. And so on.
What is particularly notable is that London is an extremely attractive place to be - or, at least, for your money to be - if you are extremely rich. The 2015 Sunday Times Rich List reported that it is home to 80 sterling billionaires, more than any other city in the world.
This may have something to do with the controversial non-domicile rule, which allows some UK residents with overseas links to limit the tax paid on earnings outside the country.
Crucially, if you happen to be Russian oligarch, it’s also located in a stable democracy where the rule of law is well established.
The last land battle on British soil took place in 1746. It endured bombardment from the air in WW1 and WW2, but occupying troops never massed at Parliament Square and foreign tanks never rolled down The Mall. For anyone of means in a more precarious political setting, the perception of permanence and dependability makes London hugely attractive.
All this has helped inflate London’s housing market, too - as did a fall in the value of sterling after the 2007 financial crash, which in effect made British property cheaper for overseas buyers. Around the same period, the Eurozone crisis and oil prices reaching $100 a barrel also meant there was a flow of capital into the city.
In the two years to June 2013, 49% of prime central London new-build purchases were to non-UK residents, according to a report by the global real estate consultancy Knight Frank.
“It's a safe bet,” says housing historian Melanie Backe-Hansen. “There's a limit to how far London can grow. Because there's a limit, these central locations are so sought after.”
And indeed it isn’t just the super-rich who are attracted to the city. People of all backgrounds from around the world flock to London in search of a better life.
From French bankers attracted by lower taxes to Eastern European labourers sending their wages home, they accounted for 36.2% of the capital’s population in 2014. By contrast, the equivalent proportions were 2% in Wales, 1.8% in the North East of England and 1.5% in Northern Ireland.
This isn’t a new phenomenon. As the trading capital of a comparably tolerant nation, the city has for centuries been a magnet for incomers from overseas.
Some were fleeing persecution, such as the Jewish migrants escaping pogroms in eastern Europe in the 19th and early 20th Century. Others were drawn into the mother country from colonial outposts, like the 40,000 Indians who were in Great Britain in the mid-19th Century. Others simply saw a place of opportunity. And so it remains.
According to the Migration Observatory, in 2013 2.8 million foreign-born people - 36% of the UK’s migrant population - lived in London. In 2009 the equivalent of half the population of 10 London boroughs moved in or out in the previous 10 years.
This churn included huge internal migration, too. In the 12 months to June 2013, 197,000 people moved in from other parts of the UK, according to the Office for National Statistics.
The peak age for these internal migrants was 23 - testament to the steady procession of young people who arrive each year seeking work and excitement.
The tale of Dick Whittington remains one of the city’s defining myths. In 2014 around 45% of graduate jobs advertised in the UK were based in London.
But in the same year, some 252,000 moved out. The most common age bracket in which people left the city was in their mid-30s - unsurprisingly, given the high cost of housing and of raising a family.
With London's population growing by about 100,000 annually, housing campaigners say London is building only about a third of the 63,000 homes it needs each year.
As a result, London’s boundaries as an economic unit now extend way beyond the greenbelt that surrounds the city.
“London might look compact but its actual field of operations, its labour market, is much bigger than it looks,” says Green. “You think about [the high-speed rail link] HS2. It's about opening the London housing market up to Birmingham and Manchester. Right now, London's commuter belt stretches all the way to Exeter.”
The only question is how long this can continue. Oil prices have fallen, and as well as the Greece debt situation some believe China’s economy is facing problems. Forecasters debate whether London’s housing market is a bubble waiting to pop.
Even assuming its current period of dominance doesn’t continue forever, London may take confidence from the fact that it has picked itself up before from catastrophe and re-emerged stronger.
And yet the perceived cultural and economic imbalance between the capital and the rest of the country is a widespread, nagging source of unease.