The Prime Minister saw off a plot to oust him when rebels admitted defeat after the local elections.
But one MP revealed they have now formally called for the PM to go and so had a number of colleagues in the past few days.
It means that although there is no formal plot, the number of disgruntled MPs acting individually could trigger a contest without any coordination.
The Conservative said: "The only question now is whether the number of letters submitted starts with a three or a four."
Only two Tories have gone on the record to say they have written to Sir Graham Brady, chairman of the 1922 committee of backbenchers, expressing no confidence in the Premier.
Former Cabinet minister Sir Simon Clarke, who has warned the party is on the "crumbling bank" of a widening precipice, claimed in March that the threshold of 52 letters had nearly been met. Former education minister Dame Andrea Jenkyns submitted a letter of no confidence last November.
The local elections were a crunch moment for Mr Sunak as plotters warned they would act if the results were dismal.
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