However they voiced concern after Mr McDonnell indicated that the leadership envisage any vote would only be on the terms of a Brexit deal.
Labour leader Jeremy Corbyn said over the weekend that he would shift his weight behind a decision to stage another Brexit referendum, should his party demonstrate clear support for the move. As delegates gathered in Liverpool, one message was emblazoned on hundreds of T-shirts and tote bags: "Love Corbyn, Hate Brexit".
But, speaking at a fringe meeting at Labour's conference in Liverpool, Mr Gardiner said it was time to "inject some realism into the debate".
"Labour have to come to a decision".
But the Prime Minister controversial Brexit plan was flatly rejected by European Union leaders at a summit in Salzburg last week.
"I tell you what: they are on borrowed time because a Labour government is coming".
"Get behind the party that made you, and join the rest of this movement in fighting to get rid of this rotten government, to give our country the fresh start it needs and make Jeremy Corbyn the people's prime minister". But what exactly they will vote on has yet to be decided, and will be crucial.
'And if the Prime Minister thinks we'll wave through a vague deal asking us to jump blindfolded into the unknown she can think again.
"Obviously I'm bound by the democracy of our party", Corbyn told the BBC.
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They are unbeaten so far with two wins and two draws, while Cultural are in sixth place with two wins, a draw and a loss.
"Labour promised to respect the referendum result, but are just playing political games and trying to frustrate it".
Labour MP David Lammy, a prominent campaigner for a second referendum, said it would be "farcical" to have a vote without the option of remaining in the EU.
"No credible plan for Brexit".
Does it deliver the "exact same benefits" as we now have as members of the Single Market and Customs Union?
Does it ensure a strong and collaborative future relationship with the EU?
Mr Corbyn declined to say which way he would vote in any new in-or-out poll, while pointing out he backed Remain in the 2016 referendum. "And no one has a clue at the moment what is going to happen".
Confirmation that the party will vote against the deal in the Commons leaves Tory whips facing an uphill battle to persuade Eurosceptic MPs to back it.
But many Labour lawmakers think his old-fashioned socialism is a turnoff for the wider electorate.
It was a tumultuous summer for the Labour Party as it was gripped by allegations of anti-Semitism. "It will make the 2016 referendum look like a walk in the park".
Campaigners for a so-called People's Vote - who staged a march in Liverpool on the conference's opening day - have welcomed the motion, which states that if Labour can not force an early general election it will "support all options remaining on the table, including campaigning for a public vote".