Jeremy Corbyn’s proposal to be installed as caretaker prime minister to prevent a no-deal Brexit has received a further blow after another senior Tory ruled out backing the plan.

Sir Oliver Letwin said he would not be able to support a bid to put the Labour leader in Number 10, saying he did not think it was likely that a majority could be formed for the idea.

The Conservative former minister, who was among recipients of a letter from Mr Corbyn outlining his plan, said it was “well worth” having discussions across the Commons to prevent the UK crashing out of the EU without a deal.

But, when asked if he would make the Leader of the Opposition prime minister, he told BBC Radio 4’s Today programme: “That appears to be his agenda, I have to say it is not one I personally share.

“I don’t think it’s at all likely that a majority would be formed for that and I personally wouldn’t want to vote for it. I wouldn’t be able to support that, no.”

Sir Oliver Letwin (Dominic Lipinski/PA)
Sir Oliver Letwin (Dominic Lipinski/PA)

However, Sir Oliver did not rule out supporting a no confidence motion to bring down the Tory government to prevent a no-deal, but said he would not back it if it led to Mr Corbyn becoming PM.

He said: “I’m not very inclined to do that if it could possibly be avoided – it’s not something I would do under any circumstances in normal life and I’d much prefer to find some other means of getting to a substantive result.”

It comes after Conservative grandee Ken Clarke said he would be willing to lead a government of national unity to avoid a no-deal Brexit – after Liberal Democrat leader Jo Swinson suggested an emergency government be led by him or Labour’s Harriet Harman.

Mr Clarke said it was “not inconceivable” that a government of national unity may be needed to resolve the impasse, suggesting politics was in a similar situation to 1931 and the two world wars.

He told BBC Radio 4’s PM programme: “If it was the only way in which the plain majority in the House of Commons that is opposed to a no-deal exit could find a way forward… I wouldn’t object to it, if that was the judgment of people, the only way forward.”

Ms Swinson’s proposal came after she rejected Mr Corbyn’s suggestion that he could lead an emergency government to thwart a no-deal Brexit, despite agreeing to meet with him to discuss a no-deal prevention plan.

Anna Soubry, leader of the Independent Group, confirmed that she would also “not support nor facilitate any government led by Jeremy Corbyn”.

But Mr Corbyn insisted again on Saturday that he should be the one to lead any caretaker government.

Speaking during a visit to Bolton, he called for “respect for the electoral process that brought about the results from the last general election”, adding: “I am the leader of the Labour Party. Labour is the largest opposition party by far. That is the process that must be followed.”

His plan has won the potential backing of the SNP, Plaid Cymru and Tory MP Guto Bebb.

SNP leader Nicola Sturgeon was among those applying pressure to Ms Swinson to re-think her position.

Sir Oliver and fellow senior Remain-supporting Tory Dominic Grieve, as well as independent MP Nick Boles, have agreed to meet Mr Corbyn.

Meanwhile a YouGov survey suggested that almost half of Britons – 48% – would prefer to see the UK leave the EU without a Brexit deal and Mr Corbyn not become prime minister, rather than him entering Downing Street and holding a second referendum.

The poll of 1,968 people taken between Thursday and Friday suggested just over a third – 35% – would, when faced with the choice, want the Labour leader to enter Number 10 and hold another referendum. The remaining 17% said they were unsure either way.