LIVERPOOL, England (Reuters) - Britain’s opposition Labour Party will vote this week to keep a second Brexit referendum as an option if Theresa May fails to pass her plan to quit the European Union through parliament, heaping pressure on a struggling prime minister.

Britain's Labour Party Leader Jeremy Corbyn speaks at a vigil for peace in Yemen during the annual Labour Party Conference in Liverpool, Britain, September 23, 2018. REUTERS/Hannah McKay

But with the leadership intent on any such referendum not allowing a re-run of a 2016 vote to stay or leave the EU, the move could reignite tensions in the party, which, like much of Britain, is divided over how to quit the bloc.

After May’s plans for Brexit - the biggest shift in British policy for more than four decades - were rebuffed by the EU on Thursday, the outcome of talks to leave are more uncertain than ever and have boosted those who want to stop the divorce.

Labour leader Jeremy Corbyn has been reluctant to support growing demands for a second referendum, or People’s Vote, but the party agreed a motion after five hours that went some way to appeasing members who want another chance to vote on Brexit.

Labour agreed late on Sunday night the party would vote on Tuesday on a motion committing the party to support “all options remaining on the table, including campaigning for a public vote” if no election is triggered by May’s Brexit plans.

For Corbyn’s backers, the motion does little to change his position that Labour prefers a new national election to a second vote, which will ask a different question from the one posed at the 2016 referendum in which the Leave campaign beat Remain by 52 percent to 48 percent.

Corbyn’s second in command, finance spokesman John McDonnell repeated that Labour was ready for an election, which he said was the “best solution”, and that any new vote would not be a repeat of the 2016 referendum to stay or leave the bloc.

The Labour Party says the motion is not “prescriptive” on what the question of any second referendum should be, leaving options open to gauge the lie of the land if, or when, such a vote needs to take place.

BABYSTEPS OR BETRAYAL?

A source in the campaign for a People’s Vote cautiously welcomed the move, saying: “We feel it’s moved in the right direction.” “It’s always going to be babysteps rather than a giant leap but it’s an important shift.”

In the opposing corner, Brendan Chilton of Labour Leave told Reuters: “There are 5 million Labour leavers in the country who will look upon this motion with dismay.”

Britain is to exit the EU in March next year after months of talks that have again exposed the deep divisions in both the country’s main parties - the Conservatives are all but at war with each other and Labour is also at odds over how to leave.

The country’s path out of the bloc is even more unclear after weeks of positive noises about the prospects of clinching a divorce deal and one on a future trading relationship, the mood between Britain and the EU turned sour on Thursday.

Slideshow ( 5 images )

Brexit minister Dominic Raab again said he was confident of clinching a deal with the EU, calling the summit in Austria last week just one of several “blips in the world”.

“They’re blown a little bit out of proportion, but we double down, we don’t throw our toys out the pram, hold our nerve, keep our cool,” Raab said.

But the summit in Salzburg seemed to increase the possibility of Britain leaving without a deal, which could hurt the economy and sever trade flows, and spurred those who want another referendum to try to overturn the 2016 vote.

May has ruled out a second referendum and EU officials say they would not want to see a re-run of the vote - prolonging uncertainty that has already forced companies to stop taking investment decisions.

And with talk of a new election swirling, May’s Conservative Party was keen to target Corbyn over his move to back a second referendum.

“Jeremy Corbyn this morning proved he is not fit to govern our country,” Brandon Lewis, the party’s chairman, said on Sunday. “He confirmed Labour would take us back to square one on Brexit.”