Lib Dem leader Tim Farron has said "people not politicians" should have the final say over the terms of Brexit.
Launching his party's manifesto, he said Brexit would have an impact "for decades to come" and the public should have the right to decide whether to go ahead with it in another referendum.
Leaving the EU single market was a "time bomb" which could "take down the NHS and schools" with it, he warned.
He told party supporters in London that the Lib Dems would not "roll over".
The Lib Dems' promise of a vote on the final Brexit deal, the centrepiece of its general election offer, would include an option to remain in the EU.
Mr Farron said the public had the choice to "change Britain's future", insisting that while he accepted the result of last year's EU referendum, he still believed the UK would be "better off and safer" within the EU.
While those who voted to leave the EU were "good, decent people", he said the Tories' approach since then had turned the UK's "friends, allies and neighbours into enemies" while Labour had "lost its purpose".
"Don't let anyone tell you the only choice at this election is between Jeremy Corbyn and Theresa May.
"The election is about your future... The more Lib Dem MPs you elect, the better deal we will get in Europe."
As well as another EU vote, the Lib Dems have pledged to reverse billions' worth of benefit cuts and pump billions of pounds into schools and the NHS in England.
To pay for the measures, they would add 1p to income tax, restore corporation tax to 20%, scrap the married couples' tax allowance and lower the level at which inheritance tax kicks in.
The Conservatives said many Lib Dem policies were "near-identical" to those put forward by Labour and would lead to higher taxes and borrowing.
On the economy, the party says it would balance day-to-day spending while reducing national debt as a proportion of GDP.
But there is no repeat of the pledge to abolish university tuition fees - the promise the party controversially abandoned when it entered coalition with the Conservatives in 2010.
In its manifesto, the party said the "fairer" system established by the coalition had led to record university application rates.
'Fight for the future'
The party, which is hoping to gather support from Remain-backing voters, believes there is no deal that could be as good as continuing EU membership and would campaign to stay in, cancelling Brexit.
Mr Farron told the BBC that Brexit represented "the biggest fight for the future of our country in a generation".
"If you don't like the deal you should be able to reject it and choose to remain in Europe."
The party, which served in government with the Conservatives between 2010 and 2015, is hoping to bounce back from its disastrous showing two years ago, when it lost almost 50 seats and was left with just eight MPs.
It has ruled out striking any coalition deals after next month's election.
It is pledging to reinstate housing benefit for 18-21 year olds, axed by the government last month, and is promoting a rental scheme under which people can build up equity with every monthly payment and eventually own their property outright after 30 years.
The plan, first mooted by the party back in 2015, envisages developers and housing associations building thousands of new homes. development bank. The total capital investment in the initiative, part of the Lib Dems' plans to build 300,000 new homes a year will be £3bn by 2022.
It will offer a bus pass discount on single and return tickets which would be available to all 16-21 year olds ordinarily resident in England, and has promised to scrap all diesel cars by 2025.
They also say they could generate £1bn from legalising and taxing cannabis. The Lib Dems say they would regulate and tax the drug - introducing limits on potency and banning sales to under-18s.
The Lib Dems have already pledged to protect per-pupil funding in England, which will cost £7bn over five years. In the manifesto it is going further, saying it will extend free school meals to all primary schools and triple funding for the early years pupil premium, boosting it to £1,000.
The party has also sought to play down remarks made by Mr Farron 10 years ago, reported in the Guardian, in which he reportedly said abortion was "wrong" and called for the law to be tightened.
Speaking to the Today programme, Lib Dem election spokesman Sir Ed Davey said Mr Farron had since changed his mind and made it clear he was pro-choice.
"We wouldn't change the law," he added.
Conservative Party chairman Sir Patrick McLoughlin said the Lib Dems would increase taxes on family homes and get rid of the Right to Buy scheme for council and social housing tenants.
"From increasing taxes to borrowing more these policies are an echo of Jeremy Corbyn's manifesto we saw earlier this week," he said.
The Green Party said it agreed with the Lib Dems' position on a second referendum but Tim Farron's party had "betrayed" young people over tuition fees and would not easily win their trust back.
Leave Means Leave, the pro-Brexit campaign group, said the Lib Dem stance was "unpatriotic and anti-democratic" and the party risked being "relegated to the obscure fringes of British politics".
The SNP suggested Lib Dem voters in Scotland were switching to them in growing numbers because they understood it was impossible for Scotland to stay in the EU while remaining in the UK.
The CBI welcomed the Lib Dems' focus on education and housing but said proposed increases to corporation tax and opposition to Heathrow expansion would not benefit business.