As activists assembled in Liverpool for their annual gathering, Jeremy Corbyn said he would still prefer to force a general election by defeating Prime Minister Theresa May's Brexit plan in the Commons.
Under intense pressure as Remainers held protests at the gathering in Liverpool, Mr Corbyn conceded yesterday that he was ready to endorse another referendum if members voted for one.
The decision comes amid the party's annual conference now taking place in Liverpool, with Brexit dominating the agenda.
But the 5,000 pro-EU protesters who marched to the conference centre in Liverpool, north-west England, highlighted the pressure he is now under to steer his party towards a second Brexit referendum.
Len McCluskey, leader of the Unite trade union, a powerful Labour ally, said British voters had chose to leave the EU and "for us now to enter some kind of campaign that opens up that issue again I think would be wrong".
The spokesman added: "If this motion is passed by delegates on Tuesday, it will show that Labour now also recognises that if an election is not possible, it will have no real option but a People's Vote".
According to the YouGov survey of 1,054 Labour members, commissioned by the People's Vote campaign, 86 per cent wanted a final, public say on the outcome of Brexit negotiations, against eight per cent who opposed it.
But with Britain due to leave the European Union in March, Brexit was likely to dominate the conference.
The weakened support for a People's Vote is despite polls showing overwhelming support within the party membership for a referendum on the final deal, and thousands turning out over the weekend to march for a final say outside the party's conference.
The Labour Party is holding its annual party conference in Liverpool, which is due to decide on decisive issues like whether to back a new Brexit referendum on the country's departure from the European Union.
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The motion was thrashed out in a tense five hour meeting of Labour officials overnight after a day in which tensions on the Brexit issue threatened to run out of control.
Labour is expected to discuss several motions on Brexit at its conference, and it remains unclear what the proposal on a second referendum might be - it could be a clear backing of a vote or something less black-and-white. "It absolutely must include the right to remain in the European Union".
"We must back it if Labour members want it", he told The Observer newspaper.
"He's got as much back bone as a jelly fish!" he said.
They are saying squarely to the leadership of the Labour Party "listen to us, hear us, give us a People's Vote".
He said his party was ready to "put our case to Parliament" for an early poll in comments likely to fuel speculation that Labour will table a vote of no confidence in Theresa May if talks with Brussels fail.
Shadow chancellor John McDonnell tells ITV News that a general election would be "the real People's Vote" on Brexit.
Mr Lammy warned that Labour needed to fight against the likes of prominent Brexiteers Boris Johnson, Jacob Rees-Mogg and Nigel Farage who, he said, have the "radical right standing behind them".
"I'm desperately trying to avoid any rise of xenophobia that happened last time around, I'm desperately trying to avoid giving any opportunity to Ukip or the far right".
"There is a lot of resentment, a lot of bitterness which I don't think will be very easily dispelled", Fielding said.