A second referendum to decide if the British people wish to plough ahead with Brexit is becoming more likely, says David Cameron’s former politics tutor.

The further vote will become a “life raft” for Theresa May and the only solution to her mounting problems over the terms of EU withdrawal, Vernon Bogdanor predicted.

The professor of government at King’s College London acknowledged a second referendum “appears unlikely at the moment”, given the Prime Minister’s determination to press ahead.

But he argued Ms May now lacks the Commons majority for the clean break with the EU she desires, following her general election setback.

Furthermore, Labour’s surprise performance – built on the “revenge of the Remainers”, as a study argued this week – suggested Jeremy Corbyn’s party could yet shift its stance.

It was plausible that the Commons could end up “deadlocked” with no majority for either a hard or soft Brexit, with the House of Lords also emboldened to throw out a hard version.

Professor Bogdanor said: “With a deadlocked parliament, the possibility of an unfavourable deal and both parties so deeply divided on Europe, it may start to appear that the only way out of the impasse is a second referendum in which the government’s deal is put it to the people for legitimation.

“That appears unlikely at the moment. Yet a referendum on Europe appeared even more unlikely when, in 1971, Tony Benn proposed it to Labour’s national executive but failed to find a seconder.

“James Callaghan presciently declared that for a divided party, the referendum might well prove a “rubber life raft into which the whole party may one day have to climb”.

“The Conservatives too may come eventually to need that life raft.”

The professor, in an article for The Guardian, also pointed out that a former Cabinet Secretary, Lord Butler, was among those arguing the public should have its say on the “outcome of the negotiations”.

“When he thought he was going to lose in 2016, Nigel Farage said that a further referendum would be needed,” he added.

“Brexit after all raises fundamental, indeed existential, issues for the future of the country. That is why the final deal needs the consent not only of parliament, but of a sovereign people.”

At present, only the Liberal Democrats are committed to holding a second referendum on any deal that emerges from the negotiations in Brussels.

At the election, Labour – eventually – ruled out such a policy, but only after confusing statements and some of its MPs are likely to be in favour.

The Prime Minister has guaranteed MPs and peers a vote on any agreement she secures in Brussels, but insisted rejection would not stop Britain leaving the EU without a deal.

However, that was before she destroyed her Commons majority – leaving her in a much weaker position and almost certainly unable to impose her will in that way.