It came as Tory rebels urged Cabinet ministers to “walk towards problems” in order to depose Boris Johnson and said the party needed senior Tories to “act as leaders”.

Three described the resignation of four senior Number 10 aides on Thursday as a “complete shambles” and predicted that it would lead to more letters of no confidence being sent to Sir Graham Brady, the chairman of the 1922 committee.

Andrew Bridgen, the Tory MP for North West Leicestershire, said:  “It’s now down to the Cabinet. Leaders walk towards problems and solve them and confront them – they don’t run away from them.”

However, an MP allied with both Mr Sunak and Mr Javid played down the significance of their public interventions, telling The Telegraph: “It is just common sense – no one sensible can defend it.”

A second source said: “What else can they say for their own credibility?”

The Telegraph understands that Mr Javid’s comments angered a number of senior figures in Number 10, who were already smarting from Mr Sunak’s comments the day before.

However, one insider said the Health Secretary’s team had quickly sought to play down his comments, adding: “He went further than he intended to.”

In contrast, the insider said Mr Sunak’s comments at Thursday’s press conference were “obviously planned”, adding: “Given what had happened, he knew it was going to be asked and he had an answer pre-prepared. I think it’s something that’s pissed them [Number 10] off rather than being an existential problem.”