The support of the main opposition party would be a major boost to campaigners for a second vote on Brexit.
Mr McDonnell stressed that Labour "respected" the June 2016 referendum result, and so any second referendum would not be another vote on whether the United Kingdom should leave the European Union or not, but on the terms of any deal negotiated by the Government.
Labour's Jeremy Corbyn has so far resisted calls to back a "People's Vote", or new referendum on the decision to quit the EU.
The leader of the British Labour Party has said he will back a second Brexit referendum if it is supported by a conference of his party.
Corbyn's close ally, Len McCluskey, leader of Britain's biggest trade union Unite, told the BBC any such second referendum "shouldn't be on: 'do we want to go back into the European Union?'" as that had been answered in the 2016 referendum.
Speaking to ITV's Good Morning Britain McDonnell said the form of the question would be decided by parliament but said "it will be about whether you accept the deal or not, or whether you send people back to negotiate a proper deal".
With more than 60 constituency Labour parties seemingly backing such a vote, activists now expect the issue to make it onto the conference agenda.
Some sections of the crowd also chanted directly at Mr Corbyn, saying: "Hey Jeremy, take a note, for the many, People's Vote".
He has always been a critic of the EU's free-trade policies and must also find a way to reconcile the traditional working-class wing of his party, who mostly voted for Brexit, and his own army of younger supporters that want to stay in the bloc.
When he suggested the Labour front bench should be "quickly sectioned at Broadmoor Mental Hospital", Clive reminded him that they were all elected MPs.
He said: "What will be put to conference is what I've been arguing for for quite a bit - that we respect the referendum, of course we do, but we want a general election".
Deputy leader Tom Watson was even firmer.
"What comes out of conference I will adhere to".
The YouGov survey of more than 1,000 Labour members found 86% support a referendum on the outcome of Brexit talks, against just 8% who oppose it.
Len McCluskey, leader of the Unite trade union, a powerful Labour ally, said British voters had made a decision 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".
Their campaign is seen by many MPs on the right of the party as an effort to purge "Blairite" influences and critics of leader Jeremy Corbyn's handling of issues such as antisemitism.
Many activists believe that with Mrs May's plans in disarray following the rejection of her Chequers proposals by European Union leaders in Salzburg, the time is now right for Labour to throw its weight behind a fresh ballot.
"There is a lot of resentment, a lot of bitterness which I don't think will be very easily dispelled", Fielding said.
Labour MP David Lammy described the motion as "farcical".
"We could well be looking towards a general election, and - do you know what? - we're ready for it".
"We very rarely have referendums in this country. They know where their members are and they know where their voters are".