Up to 30 letters of no confidence are believed to have been submitted to Sir Graham Brady, the chairman of the 1922 committee.
The prime minister faced one of his most challenging weeks to date as the Rwanda Bill was debated in the House of Commons.
Some 61 Tory MPs backed an amendment on Tuesday, proposed by former immigration minister Robert Jenrick, designed to toughen the Bill, with two deputy Tory chairman quitting their positions to vote against the government.
One of the two was also prepared to vote against the bill at its third reading, before being mocked into abstention by Labour Party MPs.
Regardless, Rishi Suank has insisted his party is “completely united” in support of the policy, as he warned peers against blocking the “will of the people”.
But insiders in the party have suggested letters of no confidence in the PM are starting to fly in.
Predicted that the Bill would not result in a single deportation flight, he told The Telegraph: “Everyone knows that the Bill is not going to work, so I think we’re going to be back to square one by August or September,” said the MP.
“I am aware, to be honest, of three or four people who have put in letters over all this, but that’s about as far as my knowledge goes. You’re probably into about 30, something like that, just from my sense of what people are saying.
“The biggest issue really is that nobody knows who they want to come next. So why would anyone submit a letter when they have not got a very, very clear idea of who follows?”
Sunak would face a vote on his leadership if 52 of his MPs, amounting to 15 per cent of the parliamentary party, submitted such letters.
Another senior Conservative MP told The Telegraph they had handed in a no-confidence letter after the proposed changes to the Rwanda Bill were rejected.
“This is basically the last shot we’ve got, the absolute last bullet in the gun,” said the MP. “There is minimum evidence that we can pull ourselves out of this tailspin.”
An MP who voted against the Rwanda Bill at its third reading said they did not intend to submit a letter “at the moment”, but added: “It’s hard to see how we will overturn Labour’s lead under this leader. I think part of the problem is there is no obvious alternative.
“I think a lot of people are regretting dispatching Boris Johnson. There’s a lot of seller’s remorse at the moment.”
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