Theresa May’s hopes of securing a cross-party Brexit deal capable of being passed by parliament have been dealt a blow after more than 80 Labour MPs warned Jeremy Corbyn that he must make a fresh referendum a red line during crisis talks with the government.

In a move that will also pile pressure on the Labour leader, the MPs said a public vote on any Brexit deal passed by the Commons should be Mr Corbyn’s bottom line during negotiations with Ms May’s team and warned that failure to insist on another referendum would be “untenable”.

The signatories include 10 shadow ministers and several prominent supporters of Mr Corbyn, including former shadow cabinet minister Kate Osamor and shadow Treasury minister Clive Lewis.

It follows days of talks between the government and Labour designed to find a cross-party solution to the deadlock gripping parliament.

The letter was organised by the “Love Socialism, Hate Brexit” group and sent to Mr Corbyn and the shadow cabinet on Saturday. It was signed by 18 of the group’s supporters in parliament, along with 62 other Labour MPs.

The move raises the prospect of dozens of Labour MPs voting against any potential cross-party Brexit deal that does not include the offer of a fresh referendum.

A similar letter to Mr Corbyn and the shadow cabinet, signed by 11 MPs, was revealed by The Independent on Wednesday.

In the latest version, 80 MPs said Ms May’s decision to seek talks with Labour was a desperate move by a prime minister who had run out of options.

Insisting that the views of party members were clear, the MPs said: “The only way to guarantee jobs, rights and protections – and Labour’s reputation with its membership and the electorate – is to support a confirmatory public vote on any option which is agreed by parliament, which will put additional pressure on the government to hold the early general election the country needs.

“Under the current leadership, Labour is offering a vision of hope which has inspired millions of people. Tory Brexit threatens this, and so does any perceived participation in delivering it. Any compromise deal which is now agreed by parliament will have no legitimacy if it is not confirmed by the public.”

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“It would be untenable for Labour not to insist on a public vote on a deal which did not meet these tests. It is not Labour’s job to rescue Theresa May and usher in her successor.

“It is our job to find a find a way to break the deadlock. In our view, the only way to do that is with a public vote. We – your supporters – urge you to make a confirmatory public vote your bottom line in negotiations with Theresa May and to fight to bring this government down.”

One of those behind the letter, Brighton Kemptown MP Lloyd Russell-Moyle, told The Independent: "This government is finished. It can't get its deal through, it's bankrupt intellectually and morally. We should bring it down, not rescue it.

"That means making a public vote a red line, and forcing an election as well. Which one will happen first I don’t know, but we need both and one will help precipitate the other in Labour's favour.”

Meanwhile, chancellor Philip Hammond insisted that he was optimistic about an agreement being reached with Labour.

In comments that will fuel fears among Tory MPs that the government could be willing to accept a fresh referendum, a customs union with the EU or the continuation of freedom of movement after Brexit, Mr Hammond said there were no “red lines” in talks with Labour.

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“We should be open to listen to suggestions that others have made,” he said. “Some people in the Labour Party are making other suggestions to us; of course we have to be prepared to discuss them.

“Our approach to these discussions with Labour is that we have no red lines, we will go into these talks with an open mind and discuss everything with them in a constructive fashion.”

The discussions continued on Saturday despite Labour warning that the government would need to show more willingness to compromise if the talks were to succeed.

Shadow home secretary Diane Abbott said the government needed to show more flexibility than it had done so far.