A cross-party Brexit deal will not get through Parliament unless it is subject to a confirmatory public vote, shadow Brexit secretary Sir Keir Starmer says.
Talks between Labour and ministers over leaving the EU continue on Monday.
But Sir Keir told the Guardian that, without a new referendum, up to 150 Labour MPs would vote against any deal.
Communities Secretary James Brokenshire said the talks should aim “to give effect to the referendum”, rather than re-opening the debate.
The UK was due to leave the EU on 29 March, but the deadline was pushed back to 31 October after MPs rejected Theresa May’s proposed deal three times.
Talks between the government and Labour aimed at finding a way out of the impasse have been going on for more than a month with little apparent headway.
Sir Keir added he would not be afraid to end the talks as soon as this week if the prime minister did not budge on her so-called red lines – positions that she feels cannot be changed in the Brexit deal.
He suggested a referendum on the final deal had become a red line of its own for many Labour MPs, saying “a significant number, probably 120 if not 150, would not back a deal if it hasn’t got a confirmatory vote”.
Labour’s stated policy is that it supports a further referendum on Brexit under certain circumstances.
It has rejected the idea of campaigning for one in any event, but will demand a public vote if it cannot get changes to the government’s deal or an election.
However, deputy leader Tom Watson agreed that with so many of his fellow MPs wanting to give the public the final say, it would be very difficult to “enforce” any Brexit agreement without another vote.
“This will only work if two very strongly-held views are plugged together – Theresa May’s deal and a confirmatory ballot,” he told Radio 4’s Today. “That is the way out of this.”
Asked whether Labour wanted to leave or remain in the EU, he replied: “We are a remain and reform party,” but “when it comes to a deal people can form their own view”.
In a speech later marking the 25th anniversary of former Labour leader John Smith’s death, Mr Watson will warn voters in next week’s European elections face a choice between Labour’s “compassionate, outward-looking patriotism” and the “nasty nationalism” of the Brexit Party.
He will reflect on Mr Smith’s pro-Europeanism and say he would have supported the view of his former deputy, Dame Margaret Beckett, and backed a “People’s Vote”.
“There are only two forces that can win this election – that nasty nationalism of the Farage Brexit Party, or the tolerant, compassionate outward-looking patriotism of the Labour Party,” he will say.
“I can only plead with Labour supporters – don’t stay at home, don’t put that cross elsewhere, don’t let them win.”
Can cross-party talks continue for much longer?
The reality is these talks have been genuine, but very difficult.
Neither side wanted to pull the plug before the local elections 10 days or so ago.
But now, as time goes on, it may well be we are reaching the moment where they have to throw up their hands and say: “We just can’t do it.”
Jeremy Corbyn and Theresa May are both on lonely tightropes trying to get across the other side of this slow-moving crisis. I think they would both like it to be over with, maybe with a cross-party deal.
But the prime minister doesn’t want to put a huge compromise on the table, she doesn’t want another referendum. Jeremy Corbyn doesn’t want to help out the government unless he can get genuine changes.
If neither of them feel they can really budge, well, the talks are not going to be able to succeed, and the government will then have to try to move on to votes in Parliament, the next part of the process.
Mr Brokenshire said the cross-party talks were about implementing the referendum result and “not somehow re-opening the debate all over again, creating even more division, more uncertainty”.
He said the shadow Brexit secretary was setting out “a slightly different message” to Labour’s “core” position on a confirmatory vote.
Labour’s position on Brexit
June 2017 – Labour’s general election manifesto accepts referendum result
March 2018 – Shadow Northern Ireland secretary Owen Smith sacked for supporting second referendum on final deal
September – Labour agrees if a general election cannot be achieved it “must support all options… including a public vote”
18 November – Labour leader Jeremy Corbyn says a new referendum is “an option for the future” but “not an option for today“
28 November – Shadow chancellor John McDonnell says Labour will “inevitably” back a second referendum if unable to secure general election
16 January 2019 – 71 Labour MPs say they support a public vote
6 February – Mr Corbyn writes a letter to Mrs May outlining five changes with no mention of a “People’s Vote”
28 February – Labour says it will back a public vote after its proposed Brexit deal is rejected
14 March – Five Labour MPs quit party roles to oppose a further referendum
27 March – The party backs a confirmatory public vote in Parliament’s indicative votes on a way forward for Brexit
30 April – Party agrees to demand a public vote if it cannot get changes to the government’s deal or an election, as it decides wording to EU election manifesto