EU referendum: Jeremy Corbyn warns of workers' rights 'bonfire' if UK leaves
Jeremy Corbyn has warned there could be a "bonfire" of workers' rights if the UK votes to leave the EU in June.
The Labour leader claimed the Conservatives would "dump" equal pay, annual leave and maternity pay rights.
And he did not think "too many people" had come to the UK from inside the EU.
David Cameron said they disagreed on "lots of things" but welcomed Mr Corbyn's backing for EU membership - as Leave campaigners said the Labour leader "does not really mean it".
Making his first major speech of the referendum campaign, Mr Corbyn stood by past criticisms of the EU but said Britain had to remain in to fight for social reform.
EU referendum: In depth
He set out an alternative, "socialist" vision for Britain in Europe to the one being promoted by Mr Cameron, who will need the support of Labour voters to win 23 June's referendum.
He called for an EU minimum wage to prevent "unscrupulous" employers from undercutting wages, and said: "Just imagine what the Tories would do to workers' rights here in Britain if we voted to leave the EU in June.
"They'd dump rights on equal pay, working time, annual leave, for agency workers, and on maternity pay as fast as they could get away with it. It would be a bonfire of rights that Labour governments secured within the EU.
"Not only that, it wouldn't be a Labour government negotiating a better settlement for working people with the EU. It would be a Tory government, quite possibly led by Boris Johnson and backed by Nigel Farage, that would negotiate the worst of all worlds: a free market free-for-all shorn of rights and protections."
Asked about concerns over high levels of immigration, he said: "There is nothing wrong with people migrating to work across the continent but there has to be a level playing field on pay and conditions. What we have is unscrupulous employers doing that."
He said a Labour government would have done more at an EU level to save the British steel industry by backing European Commission proposals to impose import tariffs on Chinese steel imports.
And he backed EU action on tax avoidance, accusing the Leave campaign of wanting to make Britain "the safe haven of choice for the ill-gotten gains of every dodgy oligarch, dictator or rogue corporation".
Mr Corbyn addressed his previous Euroscepticism, saying: "Over the years I have been critical of many decisions taken by the EU, and I remain critical of its shortcomings; from its lack of democratic accountability to the institutional pressure to deregulate or privatise public services.
"So Europe needs to change. But that change can only come from working with our allies in the EU. It's perfectly possible to be critical and still be convinced we need to remain a member."
David Cameron, manning the phones with former Labour leader Lord Kinnock and former Lib Dem leader Lord Ashdown at remain campaign headquarters, said: "I absolutely welcome Jeremy Corbyn's intervention.
"There are lots of things we disagree about, between Labour, Liberals, Greens and others, but the fact is we all come together to support the idea of Britain staying in a reformed European Union."
But Labour MP Kate Hoey, who is campaigning for an out vote, said many Labour voters shared her view and would "see through" Mr Corbyn's speech.
"We know first of all, that he doesn't really mean it, no matter how much he tries to pretend he does, and secondly, that it is not in the interest of the Labour movement," she told the BBC News channel.
UKIP said Mr Corbyn's stance on immigration made him an "outlier" within his own party, when other senior figures such as Andy Burnham recognised the need for tighter controls, and it showed he had no understanding of how "uncontrolled" mass immigration from the EU had "crushed the aspirations of so many of our people".
By BBC Political Editor Laura Kuenssberg
So far spats in the Conservative Party have dominated the conversations around our place in Europe. Labour might have lost the last election, but many of its nine million voters will look to the party for its position on the European Union.
And even though Mr Corbyn's support felt rather grudging, few of the high-profile figures are backing the institution with much affection.
Staying in is presented as the pragmatic, safer choice, rather than a source of pride and inspiration. He is not exactly alone in supporting the Remain campaign through slightly gritted teeth.
In his speech, Mr Corbyn argued that there was "a strong socialist case for staying in the European Union, just as there is also a powerful socialist case for reform and progressive change in Europe".
Asked why he had been converted to the EU cause, after speaking against it so many times in the past and voting to come out in the 1975 referendum, he said the Labour Party and trade unions had "overwhelmingly" decided to back EU membership "and that's the party I lead and that's the position I am putting forward".
But he said there was "nothing half-hearted" about Labour's campaign and said he would continue to make the case for membership in the run up to polling day.
Mr Corbyn told the audience of Labour supporters: "You cannot build a better world unless you engage with the world, build allies and deliver change. The EU, warts and all, has proved itself to be a crucial international framework to do that.
"That is why I will be am backing Britain to remain in Europe and I hope you will too."
The Labour leader was heckled by a Conservative voter during his speech. Stephen Wolstenholme, who was filming the event for his YouTube channel, interrupted Mr Corbyn to claim environmental regulations could be improved on a UK level.
After the speech, Mr Wolstenholme said he was a supporter of the Labour Out campaign and wanted to see Mr Corbyn give a "Tony Benn-style left wing case for coming out".
Ahead of the EU referendum campaign's official beginning on Friday, Vote Leave and Britain Stronger in Europe have been designated as the official Leave and Remain campaigns by the Electoral Commission.
Meanwhile, Leave.EU - a supporter of pro-exit group Grassroots Out which lost out to Vote Leave - announced it did not plan to launch a judicial review of the Commission's decision.