Andrea Jenkyns MP – the Tory backbencher who has been a consistent critic of Mr Sunak – said more than two dozen colleagues had told her they have handed in letters.
Reports suggest several Tories have submitted no-confidence letters to the party’s all-powerful 1922 Committee – which decides on leadership contests – since the tense Rwanda bill vote.
While only 11 Tory MPs voted against the bill earlier this week, there is wider frustration among right-wingers over the legislation and dire YouGov polling which shows the party heading for a 1997-style wipeout.
Ms Jenkyns said Mr Sunak was a “gift to Labour” as she urged fellow right-wingers to “act” on murmurings of a push against his leadership. She told GB News: “We’ve got to replace Rishi.”
“Even though he won that vote ... I’m hearing that more letters are going in today, and I still think he’s on borrowed time,” said the staunch Johnson loyalist, who voted against the Rwanda bill. “I’d be very surprised if he’s taking us into the election.
She claimed: “A couple of weeks ago I did a tally, it was about 29 MPs who told me, but that was pre this disastrous polling, what we’ve seen at the weekend and pre this Rwanda farce, what’s happened the last 24 hours. So I’m sure that more has gone in since the weekend.”
However, Tory moderates have dismissed Ms Jenkyns claims about no-confidence missives being sent to 1922 Committee chair Sir Graham Brady.
“Talk of letters is always nonsense – only Sir Graham knows how many are in,” one Sunak ally told The Independent. The senior Tory said it would be “madness” to replace another leader before the general election.
1922 Committee rules mean Mr Sunak would only face an embarrassing vote on his leadership if 52 Tory MPs –15 per cent of the parliamentary party – submit letters.
The row comes as Mr Sunak again urged peers to “crack on” with the Rwanda bill in the House of Lords – saying he wanted to get the deportation flights “up and running” as soon as possible.
In a pointed message to the Lords, the PM said on Friday: “And I would urge them strongly to crack on with it because we all just want to get this done ... The country is fed up and frustrated with the merry-go-round on this topic.
However, peers have rejected the Tory leader’s demand to rush approval. The upper chamber has approved a two-month timetable to scrutinise – refusing to move any more quickly than usual.
The bill will get its second reading in the upper chamber on 29 January. And a final vote is set for 12 March, before the stage known as “ping-pong” between the Commons and Lords. It means it is unlikely to make it into law before later March.
Labour’s leader in the Lords Angela Smith said Mr Sunak’s Thursday press conference was “bizarre”, and insisted that “we will stick to our normal processes”.
Lord Carlile, a cross-bencher peer, said his colleagues were oblige to try to rewrite the bill and “kill it” if necessary.
But such defiance usually has little bearing on reality. Labour has said it will not try to block the bill in the Lords, so the chamber is expected to pass it largely unamended.
Meanwhile, Mr Sunak is under fire from Labour after he was captured laughing when challenged in the street by a woman who expressed her anger on the state of the NHS.
Mr Sunak burst out laughing as the Winchester woman – a former NHS worker – told him he could stop the problems and “make it all go back to how it used to be”.
Labour pounced on the uncomfortable clip and said it showed that the Tory leader “has no idea of the misery NHS patients are going through”.