Labour is on the brink of a major bust-up if Jeremy Corbyn fails to demand a second referendum as the price for any Brexit deal struck with Theresa May.

A string of senior figures – including shadow foreign secretary Emily Thornberry – believe securing a public vote is an absolute must, while 12 MPs, including four frontbenchers, have written an open letter to Mr Corbyn in The Independent saying “it would be untenable for Labour not to insist” on one.

As Mr Corbyn was in the prime minister’s office holding the talks, one of his party’s biggest trade union backers also endorsed a motion calling for a confirmatory referendum on any deal.

But key individuals on the Labour side of the talks indicated a new vote may not be one of his asks, with one shadow cabinet member attending having stated hours earlier that a deal endorsed by the party would not need a referendum.

It comes despite Labour, and indeed Mr Corbyn himself, backing a motion in the House of Commons days ago which called for a referendum on any Brexit plan passed by parliament.

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The Independent has been pushing for a new referendum through its Final Say campaign, and has backed both major marches through central London demanding one.

On Wednesday Mr Corbyn was accompanied by his chief whip Nick Brown, Brexit spokesman Sir Keir Starmer and shadow business secretary Rebecca Long-Bailey to the talks, to which Ms May invited him on Tuesday night in a major strategic shift.

Neither side had been prepared to set out a specific position in advance of the talks in an effort to be constructive, but as news of the meeting sank in on Wednesday, Labour backers of a new referendum were clear that it should be a fixed demand.

In a letter published in The Independent the 12 MPs who describe themselves as Mr Corbyn’s supporters and are now organising into a parliamentary “Love Socialism, Hate Brexit” group, saying: “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.”

The views of members are clear. Labour’s democratically established policy, passed at party conference in September 2018, is to oppose a Brexit deal which does not meet Labour’s six tests and put any deal that does to a public vote. It would be untenable for Labour not to insist on a public vote on a deal which did not meet these tests Eleven Labour MPs

They argue that Ms May has come to Labour for talks to “bail her out” after she failed to pass her own deal through the Commons, but they claim any guarantees she gives will not be watertight and could be overturned by a future leader.

The MPs say the only way to guarantee Labour’s reputation with its membership and the electorate is by giving the public a Final Say on any Brexit deal agreed by parliament.

It adds: “The views of members are clear. Labour’s democratically established policy, passed at party conference in September 2018, is to oppose a Brexit deal which does not meet Labour’s six tests and put any deal that does to a public vote.

“It would be untenable for Labour not to insist on a public vote on a deal which did not meet these tests.”

In the final line the MPs say: “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.”

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On 27 March when the Commons voted on a series of different Brexit outcomes, the plan for a confirmatory referendum won the largest amount of support – with 198 Labour MPs backing it.

One senior Labour figure told The Independent: “It was only a few days ago that 80 per cent of the parliamentary party backed that motion calling for a vote on any deal.

“How can we possibly now agree to helping Theresa May deliver Brexit without one? Party members would go spare.”

In a letter received by MPs on Wednesday , Ms Thornberry, who was meant to attend the meeting with Ms May, said: “What I would have said is that if we look like reaching any other decision than confirmatory vote, that would be in breach of the decision made unanimously by conference.”

Unison, which handed Labour £1.1m last year, also piled on the pressure by backing a call to put any plan agreed by parliament back to the British public.

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Earlier in the day party grandee Margaret Beckett, who spearheaded the 27 March motion, said Mr Corbyn should abandon negotiations if Ms May refuses to discuss a referendum.

Appearing at a press conference organised by the People’s Vote campaign for a fresh referendum, Dame Margaret said Mr Corbyn was now in “a very powerful position”.

Asked if the Labour leader should walk out of talks if the PM failed to offer a second vote, Dame Margaret told The Independent: “If she says that this is a condition that we don’t even discuss it, then yes, I think he should.

“Maybe she has got more sense than that, you just never know.”

On Saturday, the demand for a public vote on any deal was echoed by the party’s deputy leader Tom Watson, who said: “Whenever a final deal is reached, and whatever that deal eventually looks like, I think this question can only be truly settled by giving the decision to the people.

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“Our plan to put any final Brexit deal back to the people has already begun to unite the Labour Party. And, if the last referendum divided our country, I believe a new one might help heal it.”

It was also only 10 days ago that Sir Keir said that “no one should doubt” his commitment to Labour’s policy, adopted at party conference, that a referendum would remain an option should the party fail to force a general election.

“What the party has said is there must be a public vote and we said we’d either put down an amendment ourselves or support an amendment, and that needs to be between a credible leave option and remain,” he said.

Speaking after prime minister’s questions on Wednesday, Mr Corbyn’s spokesman was asked whether a new vote would be one of his demands and answered that Labour’s position was to call for a new public vote only to stop a “damaging Tory Brexit” or a no-deal situation.

It was put to him that Mr Corbyn would be unlikely to agree to a deal he would describe as damaging, and also that any agreement struck would preclude no deal, meaning that if Labour did come to an understanding with Ms May, the party’s stated position would exclude a referendum – in response the spokesman restated the party’s position.

Earlier in the morning Ms Long-Bailey said: “If we get exactly what we want ... then I would struggle to find a reason to put that to a public vote.”

At a Commons committee around the same time, Brexit secretary Stephen Barclay said it would take around a year to legislate for a fresh public vote – a timeframe that has previously been disputed. He said: “You have got to pass the primary legislation, you have got to resolve the issues with the Electoral Commission, you have got to have the purdah period in the run-up to any referendum.”

Speaking after the discussions between Ms May and Mr Corbyn, a Downing Street spokesperson said: “Today’s talks were constructive, with both sides showing flexibility and a commitment to bring the current Brexit uncertainty to a close. We have agreed a programme of work to ensure we deliver for the British people, protecting jobs and security.”