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. But the political landscape has changed since May was ambushed by the European Union on Thursday over her plans for Brexit – the biggest shift in British policy for more than four decades, Reuters reported.
With talk of a new election swirling after May's "Chequers" plan was all but shredded at an EU summit in Austria last week and chances of Britain exiting the bloc without a deal rising, Labour is under pressure to start setting the Brexit agenda.
Corbyn, a veteran eurosceptic who in 1975 voted "No" to Britain's membership of the then-European Community, said that while he would listen to a debate about any possible second vote on Britain's membership, he preferred a snap election if May failed to get a deal that Labour could support in parliament.
"Our preference would be for a general election and we can then negotiate our future relationship with Europe but let's see what comes out of conference," he told BBC, saying Labour was ready to vote against any deal.
"We would vote it down if it didn't meet our tests in order to send the government, if it is still in office, straight back to the negotiating table and if there is a general election and we are in office we would go straight to the negotiating table."
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.
Britain is to exit the EU in March. After weeks of both sides making positive noises about prospects of clinching a divorce deal and their future trading relationship, the mood turned sour on Thursday in Salzburg, Austria, when the bloc's leaders, one by one, came out to criticize May's Chequers plans.
A tacit agreement to try to offer her some support before she heads to what is going to be a difficult annual conference of her governing Conservative Party later this month was broken by some British diplomatic missteps.
May says she will hold her nerve in the talks, pressing the EU to come up with an alternative proposal to her Chequers plan, named after the prime minister's country residence where a deal was hashed out with her top ministers in July.
But the impasse with the EU has prompted some to predict an early election, with local media reporting that May's team has begun contingency planning for a snap vote in November to save both Brexit and her job.
Brexit minister Dominic Raab again ruled out a new election, describing the suggestion as "for the birds". He said Britain would not "flit from plan to plan like some sort of diplomatic butterfly".
"We are going to be resolute about this," Raab added.