It comes as Mr Corbyn steps up planning for an autumn election, meeting union leaders to set out a manifesto policy which would see the party offer a referendum choice between “credible” Remain and Leave options without committing itself to backing either side.
But Mr Watson, in a speech on Wednesday in London, will insist that if an election comes first, Labour should fight it “unambiguously and unequivocally” backing Remain.
Meanwhile, there were signs of increased interest in a referendum on the Tory side, with expelled former cabinet minister Oliver Letwin throwing his weight for the first time behind a public poll and suggesting that Boris Johnson might be “flexible” enough to shed his opposition to a Final Say vote.
Mr Letwin told BBC Radio 4’s Today programme: “It’s pretty clear that there is a huge number of Labour MPs, Lib Dem MPs and SNP MPs who would vote for any reasonable deal subject to a referendum.
“I think there is now an increasing number of Conservatives and ex-Conservatives who would as well, so I think there is a majority there too.”
He acknowledged that Mr Johnson had repeatedly ruled out a Final Say vote, but added: “Boris has often changed his mind about many things – that’s one of his advantages, that he is very flexible – so maybe he can.”
One senior People’s Vote source indicated that the campaign believes that Mr Letwin may be the first of a series of expelled Tories to back a referendum, adding momentum to calls for a Final Say ahead of a major march in London on 19 October.
Mr Corbyn and other opposition leaders have twice voted down Mr Johnson’s calls for an election in October to “let the people choose” who should negotiate Britain’s final deal in a Brussels summit days before the Halloween deadline for departure.
But once a no-deal outcome on 31 October has been averted, the Labour leader is expected to give the green light for an election in November or December in which Brexit would dominate debate.
He told union leaders in a private meeting in Brighton on Tuesday that Labour’s manifesto would deliver a message to both Leave and Remain voters that they can vote for the party and keep their favoured Brexit option on the table.
His comments have fuelled expectations that Labour MPs and frontbenchers might be allowed to campaign on either side in any referendum, with Mr Corbyn himself remaining aloof as Harold Wilson did in the Common Market vote of 1975.
But Mr Watson will attempt to put the brakes on the headlong rush towards an autumn poll, insisting Mr Corbyn must continue to hold out against an election until the Brexit issue is settled by a Final Say vote.
He will warn that an election before Brexit is resolved would allow the “braying bullies of the Tory leadership” to drown out Labour’s messages on austerity, the NHS, crime and poverty without providing a clear-cut judgment from voters on the EU issue.
“A ‘Brexit election’ might at this moment seem inevitable, but that doesn’t make it desirable,” Mr Watson will say. “Elections should never be single-issue campaigns.”
“Boris Johnson has already conceded that the Brexit crisis can only be solved by the British people. But the only way to break the Brexit deadlock once and for all is a public vote in a referendum. A general election might well fail to solve this Brexit chaos.”
Shadow Brexit secretary Sir Keir Starmer will leave no doubt that Labour is gearing up for an imminent election when he tells the TUC Congress on Wednesday that the party will be “ready” to go to the country soon after parliament returns from its suspension on 14 October.
“We have to stop no deal,” Sir Keir will say. “Last week we beat them in parliament, but very soon we will have to beat them at the ballot box.”
Sir Keir will also say he expects Brexit to be a “crucial” issue at the election and confirmed that Labour believes a referendum with Remain on the ballot paper is the only way to “break the deadlock and clean up the mess left by the Tories”.
But there were warnings from the backbenches that an election before Brexit is settled could be fatal for Labour.
One senior MP who backs a Brexit deal said: “It’s an existential issue for us. If Brexit is still in play at the election we could be wiped out in the midlands and the north, losing anything up to 80 seats. And if there is no clarity about what we stand for it will only be worse.”
Former prime minister Tony Blair also urged caution over an early election, warning it would may well result in another hung parliament which fails to establish the public’s preferences on Brexit.
“If parliament is blocked over Brexit and to deblock it you need to go back to the people, go back to the people on the issue of Brexit,” he said.
“Go back and ask them whether they want the government’s proposition or whether they want to stay. That’s the obvious way out of this.”
Arguing for a fresh public vote, Mr Watson will say that, after more than three years, the 2016 referendum result is “no longer a valid basis on which to take such a momentous decision about the future of the United Kingdom”.
“The only proper way to proceed in such circumstances is to consult the people again,” he will say.
If a general election comes first, “we must unambiguously and unequivocally back remain ... not for electoral or tactical reasons, but because it is the right thing to do for the country at this time of greatest crisis since the Second World War”.
James Cleverly, the Conservative chairman, said it was clear that Labour “want to cancel the referendum result”.
“This latest trick would mean delaying Brexit again for up to a year, handing over £250m a week to Brussels for no purpose,” said Mr Cleverly. “Labour are running scared of an election and only offer more dither and pointless delay.”
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