Ed Miliband led a clutch of senior party figures in insisting Brexit was not the solution to widespread concerns over the impact of immigration.
Deputy leader Tom Watson published an analysis claiming the Conservatives would be forced to hike VAT and slash spending to cover a £28 billion “black hole” in the public finances.
The concerted move came amid concerns within senior party circles that Jeremy Corbyn has been only lukewarm in his backing for Remain and that support for Leave among traditional Labour voters could be decisive in the referendum on June 23.
Mr Miliband admitted the result of the referendum was “in question”, saying: “That’s why the Labour message has got to be heard, and I think so far not enough of our voters have heard that we are for in, and for Remain.”
Those concerns were intensified with the announcement that two prominent backbenchers – John Mann and Dennis Skinner – have joined the handful of Labour MPs in the Brexit camp. Reports suggest the party’s own analysis has uncovered stronger than expected support for leaving the EU among members.
In a keynote speech in London, Mr Miliband accused Leave campaigners like Boris Johnson and Michael Gove of trying to “perpetrate a fraud” on the electorate by claiming to be standing up for the rights of workers and the NHS.
Leaving the EU, he said, would set back the cause of social justice for “decades to come” with “dire consequences” for working people as the Conservatives tore up workplace protections.
While he acknowledged that immigration was a concern for many Labour voters, he said the Brexit camp were only offering “false solutions” to the issue.
“False solutions are no solution, and that includes leaving the EU with all the economic consequences it would have for working people. Instead we should act here at home to tackle the exploitation and undercutting of wages, which we can do,” he said.
“And we should tell the truth: which is that the problems of the NHS, housing, schools and the next generation are much less about people coming here and much more about a Conservative government.”
The Remain camp was bolstered by a warning from Germany’s finance minister that the UK would not have access to the single market if it was outside the EU.
Wolfgang Schaeuble said a relationship of the kind enjoyed by Norway or Switzerland “won’t work” for Britain.
“If the majority in Britain opts for Brexit, that would be a decision against the single market. In is in. Out is out. One has to respect the sovereignty of the British people,” he said.
However, Mr Watson acknowledged that while Labour was “as united as it possibly can be” in backing Remain, the message was not getting through to voters.
“The one thing that does concern me is that the polls seem to say that about 40 per cent of Labour supporters don’t yet know our position,” he said at a campaign event in London.
With many MPs predicting David Cameron will be forced to quit if there is a vote for Leave, Labour issued an analysis of what a Conservative government led by Mr Johnson with Mr Gove as chancellor might do.
It claimed they would be faced with a “Tory Brexit black hole” in the public finances which they would fill through fresh austerity measures and tax rises.
It suggested that to deal with a £28bn shortfall, VAT would rise to 22 per cent, costing the average family £360, while spending would be slashed and cuts to payments for the disabled would be “back on the agenda”.