Shadow chancellor John McDonnell has signalled Labour will whip its MPs to back a bid for a new Brexit referendum.
Labour divisions on the issue were thrown into sharp focus as former minister Caroline Flint estimated up to 70 of the party’s MPs are opposed to a second national EU withdrawal poll.
Mr McDonnell said on Sunday: "Normally we will whip and that will be decided in the normal way by the chief whip and the shadow cabinet and the party overall.
"I think on an issue as this we would see a whip but also you’ve got to respect people’s views and their constituency interests as well, and the whipping arrangement will be determined in discussion in due course," he told Sky News.
Meanwhile Theresa May has received a Brexit boost as the head of the influential 1922 Committee of backbench Tories signalled support for her stance.
Sir Graham Brady indicated he could swing behind the Prime Minister’s Withdrawal Agreement ahead of crunch Commons votes.
Writing in the Mail on Sunday, Sir Graham said: "The whole country is tired of vacillation and delay.
"When the right compromise is offered, we should pull together behind the Prime Minister and help her to deliver our exit from the European Union on March 29."
ITV News Political Correspondent Dan Hewitt explains why MPs are softening their position over Mrs May's Brexit deal particularly arrangements surrounding the Irish backstop.
He said instead of removing the backstop entirely MPs could compromise and vote on a legally binding change to the backstop which would make it temporary.
He added: "Theresa May, to get her deal through, needs the support of her Brexiters and her backbenchers and the most senior backbencher is Sir Graham Brady."
The PM said if her deal is rejected, MPs will be able to vote on whether the UK can leave the EU in a no-deal scenario, and if that is rejected, the Commons can decide on whether to extend Article 50 and delay Brexit.
In a message to Labour MPs on Brexit, former prime minister Tony Blair told BBC1’s Andrew Marr Show: "Vote against the deal, use an extension to come to a conclusion - hard versus soft or back to the people.
"I think you’ll get to another referendum when people understand that a hard Brexit is going to be deeply economically painful for the country and a soft Brexit means we just become a rule-taker.
"It’s in those circumstances that I think you mobilise a majority in Parliament to say the sensible thing in these circumstances is to put it back to the people, or pass her deal subject to a confirmatory referendum."
The hardline European Research Group (ERG) of Tory MPs led by Jacob Rees-Mogg also indicated a more conciliatory tone on the issue.
The ERG has drawn up “three tests” the Government must pass to win backing, according to the Sunday Times.
In private talks with Attorney General Geoffrey Cox, the ERG called for a legally-binding mechanism to escape the backstop, with a clear exit route and an unambiguous rewrite of the language in the Government’s legal advice, the newspaper said.
The stance has been drawn up in conjunction with the DUP, according to the Sunday Times.
Many Brexiteers have expressed opposition to the backstop as it would leave the UK obeying EU customs rules if no wider trade deal is agreed after a transition period.