Labour has unveiled pledges costing £48.6bn - to be funded from extra tax revenue - in its election manifesto.
Leader Jeremy Corbyn said the manifesto - including billions for schools and the NHS and an expansion of free childcare - was a "programme of hope".
The income tax rate would rise to 45p for earnings above £80,000 and then to 50p in each pound earned over £123,000.
It also includes the nationalisation of England's water companies and scrapping university tuition fees.
Labour said all the pledges were costed, with other fundraising measures including corporation tax rises, a crackdown on tax avoidance and an "excessive pay levy" on salaries above £330,000.
But the Conservatives said working families would "pay the price" for what they said were a series of unfunded spending commitments.
Launching the proposals in Bradford, the Labour leader said "whatever your age or situation, people are under pressure, struggling to make ends meet. Our manifesto is for you."
Mr Corbyn joked about last week's leak of a draft of the proposals and then said Labour would not increase VAT or National Insurance, with income tax rises reserved for the "richest 5% of high earners".
The manifesto, the first to be announced by one of the major parties ahead of the 8 June election, also includes:
- Taking Britain's railways back into public ownership
- Moving towards a publicly owned energy system
- The "reasonable management" of immigration and no "bogus targets"
- Building 100,000 affordable homes a year
- Supporting the renewal of the Trident nuclear weapons system
- Offering an immediate guarantee about the status of EU nationals in the UK
- Refusing to leave the EU with no deal in place
- A review into reforming council tax and business rates, in favour of options such as a land value tax.
Mr Corbyn said he was confident that once voters could "study the issues" they would conclude: "That the few have prevailed over the many for too long.
"And that they will decide it is now time for Labour."
Paul Johnson, of the Institute for Fiscal Studies, said it was "genuinely uncertain" whether increases to income tax would raise the £6.4bn Labour has earmarked, adding that they represented a "big increase" for high earners.
Analysis: New direction of travel
BBC political editor Laura Kuenssberg
Jeremy Corbyn stunned his party hierarchy by becoming its leader. Now he has shown how he hopes to change the country.
It is his manifesto, very much his manifesto, with some senior members of the shadow cabinet still in the dark about the precise details about the big decisions on tax this morning.
And his manifesto represents a break from the political direction of travel that has dominated British politics for years - moves towards higher, not lower tax, a bigger, not smaller state, a move from what Labour had considered the centre ground.
One senior Labour figure told me you wouldn't expect him to do anything other than paint on a big canvas.
But it's the public who will decide if the picture is to their taste next month. Mr Corbyn's team hopes the problems and pressures of 2017 Britain have recast the electorate, and it is eager for something different.
On welfare, Labour said it would "act immediately to end the worst excesses of the Conservative government's changes", including scrapping the so-called bedroom tax and restoring housing benefit for under 21s.
Mr Corbyn told BBC political editor Laura Kuenssberg that £2bn would be spent on the "worst effects" of the cap on benefits.
"You will see a lot of changes on it," he said.
"But bear in mind we've had two weeks in order to prepare all of these policy issues because of the speed in which the election has been called.
"I accept the challenge. We've produced I think a very well thought out and very credible manifesto in a very short space of time. I think we deserve some credit for that, actually."
Labour said it would return the railways to public ownership as franchises expire, or in some cases using franchise reviews or break clauses.
The manifesto did not set out how its plans to nationalise the national grid and the water industry would be funded.
Shadow cabinet member Sarah Champion told the BBC the water proposal was "an intent" and that Labour would "need to look at the legislation".
Labour has already made a series of tax pledges, including increasing corporation tax from 19% to 26% and a "Robin Hood" tax on financial transactions, to fund multi-billion pound spending commitments on health, education and policing.
The manifesto also includes a pay levy designed to discourage companies from paying "excessive" salaries.
Companies paying staff more than £330,000 will pay a 2.5% surcharge while salaries above £500,000 will be charged at 5%. Labour has said the move, designed to reduce pay inequality by bearing down on "very high pay", will only apply to firms with "high numbers of staff".
Speaking on a visit to Stoke-on-Trent, Prime Minister Theresa May said Labour's sums did not add up and people should be "worried" about what would happen if they won power.
"What we see is actually these policies, they are not sensible economic policies and would actually damage our economy," she said.
SNP deputy leader Angus Robertson claimed the manifesto was full of "headline-chasing policy announcements" - adding that many of the pledges were already being delivered in Scotland by the SNP administration.
Liberal Democrat former cabinet minister Alistair Carmichael condemned Labour's approach to Brexit, accusing it of "failing to stand up for our membership of the single market and refusing to give you the final say over the Brexit deal".