Labour has launched its general election manifesto, promising to "transform" the UK and to renationalise rail, mail, water and energy.
Leader Jeremy Corbyn also vowed "a green transformation" of the economy, aiming to get the UK "on track" for a net-zero carbon system by the 2030s.
The 105 page manifesto includes a windfall tax on oil firms and scrapping rises in the state pension age.
Mr Corbyn said his offer to voters was "radical" and would mean "real change".
He accused "bankers, billionaires and the establishment" of wanting to thwart his plans, adding: "They don't own the Labour Party. The people own the Labour Party."
On Brexit, Labour says it wants to renegotiate a new Brexit deal, incorporating a close relationship with the EU, which would then be put to a "legally binding" referendum.
On Scottish independence, the party says it would not grant permission for a referendum on the issue "in the early years" of a Labour government.
BBC economics correspondent Dharshini David said Labour's manifesto pledges would add £83bn to annual government spending by 2024.
The party said this would be paid for by tax increases on higher earners and reversing corporation tax cuts.
What is in the Labour manifesto?
- £75bn to build 150,000 new council and social homes a year, within five years
- An immediate 5% pay rise for public sector workers, with year-on-year above-inflation pay rises to follow
- Introducing a "real living wage" of at least £10 an hour
- Reviewing the retirement age for people in hard manual jobs
- Introducing a second homes tax
- Reversing inheritance tax cuts and imposing VAT on private school fees
- Giving EU nationals living in UK the automatic right to stay
- Reinstating 3,000 bus routes that have been cut
- Free broadband for all, delivered by part-nationalising BT
- A £3bn plan to offer adults in England free access to retraining
- A pledge to reduce all primary school classes to fewer than 30 children
- Free personal at-home care in England for over-65s most in need of it
- A pledge to renew the Trident nuclear deterrent and spend at least 2% of GDP on defence
- Reducing the voting age to 16
Speaking at Birmingham City University, Mr Corbyn insisted Labour's policies were fully costed and "popular".
But there has been internal controversy over the idea of a one-off tax on oil companies, with some trade union officials fearing it would damage Scotland's North Sea Oil industry.
Mr Corbyn is promising to set up a £250bn Green Transformation Fund - to be paid for through borrowing - to fund 300,000 new "green apprenticeships" and loans for people to buy electric cars.
And Labour is promising to "achieve the substantial majority of our emissions reductions by 2030 in a way that is evidence-based".
An ambitious plan, but is it credible?
This is without doubt the most ambitious - and most costly - manifesto I've ever seen. Radical it absolutely is, but the question is: is it credible or affordable?
Labour says yes, by introducing higher taxes on the wealthy and big businesses.
But we live in a globalised era when the wealthy can move their money around. Would they leave their cash in a Labour Britain that was going to tax them more?
Another credibility question that centres on Jeremy Corbyn is whether is he the leader to deliver this, given he won't answer the most basic, fundamental political question of our time, which is: "Are you for or against Brexit?"
'We will deliver'
Mr Corbyn said it was a "manifesto of hope", adding: "Over the next three weeks, the most powerful people in Britain and their supporters are going to tell you that everything in this manifesto is impossible.
"That it's too much for you. Because they don't want real change. Why would they? The system is working just fine for them. It's rigged in their favour."
The party is hoping its manifesto will help it get back into power for the first time since 2010, but the opinion polls so far suggest it is heading for defeat on 12 December.
Labour is locked in a battle with the Conservatives - who are also promising to borrow money to spend on public services - in seats across the Midlands and the north of England.
In his speech, Mr Corbyn said voters could trust his party to deliver its pledges because "we're opposed by the vested interests for standing up for a different kind of society".
"We'll deliver real change for the many, and not the few," he said.
Responding to the manifesto launch, the Conservatives said: "A Corbyn-led government would mean higher taxes, the chaos of two more referendums, and frightening levels of debt."
A spokesman added that "hardworking taxpayers" would be left to "foot the bill".
Lib Dem Brexit spokesman Tom Brake said Mr Corbyn's wider plans would be "badly damaged" if Labour took the UK out of the EU.
He added that "the extensive plan of nationalisation" would "keep government locked down for years".
Watch the BBC Question Time leaders' special
Head of the business group CBI Carolyn Fairbairn said they shared Labour's ambitions on "a close trading relationship with Europe and a fairer, greener and more inclusive economy at home".
However she warned the party's "default instinct for state control will drag our economy down".
Paul Johnson, director of the IFS, said there were "risks" with both the proposed spending increases and tax rises.
"It will be extremely hard simply to deliver anything like this scale of increase in capital spending, at least in the near-term, certainly in an efficient and cost effective way," he added.
But trade union boss Frances O'Grady praised Labour's manifesto, saying it "puts working families first" and "paves the way for higher pay for everyone".
What are the other parties pledging on Brexit, carbon neutrality and housing?
Brexit: The Conservatives say they will deliver Brexit by the end of January 2020 under the terms of the PM's deal negotiated with the EU.
The Liberal Democrats have vowed to cancel Brexit if elected as a majority government, or otherwise campaign for a referendum including the option of staying in the EU.
The SNP wants Scotland to stay in the EU. The Brexit Party wants the UK to leave immediately without an exit deal, but negotiate a free trade agreement with the EU.
Carbon neutrality: The Conservatives have said they want to achieve net zero emissions by 2050, while the Liberal Democrats have pledged to achieve this by 2045.
The Green party has gone even further, by aiming for carbon neutrality by 2030. The SNP says it wants a 100% reduction in emissions as soon as possible.
Housing: The Liberal Democrats say total house building should rise to 300,000 homes each year, a third of which should be for social rent.
The party wants to allow social renters to use their rent payments to build up a stake in their property, and give government-backed loans to first-time renters to help with tenancy deposits.
The Conservatives have announced measures which they say will boost private house building, promising a million homes over the next five years.
They have also pledged to "work with investors and others" to increase the availability of long-term fixed rate mortgages up to 95% of a house's value.
What are the parties promising you?
Here's a concise guide to where the parties stand on key issues like Brexit, education and the NHS.
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