Expelled Tory heavyweight Oliver Letwin has thrown his weight behind a fresh Brexit referendum and told Boris Johnson it is his best escape route from the crisis.

The former cabinet minister said there was “an increasing number of Conservative and ex-Conservative” MPs now ready to deliver a majority for a further public vote, with parliament deadlocked.

Sir Oliver said the prime minister has demanded to “take it back to the people” – but argued the general election he craves would fail break the impasse.

“There is another option of course which is to bring back a deal and ensure a majority for it by attaching it to a referendum,” he suggested.

“Why not get a deal in front of parliament? If parliament won’t otherwise accept it, why not take it to the people in a referendum and let’s see.”

Many Labour MPs have long been willing to vote for a Brexit deal provided it was rubberstamped – or rejected – in a Final Say referendum, but failed to persuade Theresa May to make the leap.

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Now Sir Oliver, one of the 21 Tories sacked for last week for moving to block a no-deal Brexit, has urged her successor to swing behind the strategy.

“It’s pretty clear that there is a huge number of Labour MPs, Lib Dem MPs and SNP MPs who would vote for any reasonable deal subject to a referendum,” he told BBC Radio 4’s Today programme.

“I think there is now an increasing number of Conservatives, and ex-Conservatives, who would as well, so I think there is a majority there too.”

The former cabinet office minister acknowledged the prime minister had ruled it out, but added: “Boris has often changed his mind about many things – that’s one of his advantages that he is very flexible – so maybe he can.”

Any U-turn is unlikely to come before late October at the earliest, after parliament was finally prorogued shortly before 2am on Tuesday, amid chaos and disorder.

The battle for Brexit is heading for the courts, with Mr Johnson set to defy MPs’ instruction to seek an Article 50 extension if they have not passed a deal by 19 October.

The prime minister insists he still wants an agreement and will hold talks with Donald Tusk, the outgoing European Council President at the United Nations, the week after next.

Bilateral talks with Angela Merkel, the German chancellor and French president Emmanuel Macron are also likely, plus a possible first trip to Brussels next week, to meet Jean-Claude Juncker, the European Commission president.