Lord Blackwell, a former head of Sir John Major’s policy unit, said Mr Johnson should “radically slim down” his Downing Street operation, which has ballooned to incorporate 400 employees.

Writing for The Telegraph, he said: “Building up of staff within No 10 works against the spirit of collective Cabinet government.”

Mr Doyle, Mr Rosenfield and Mr Reynolds have all been directly caught up in the ‘partygate’ scandal.

However, it was claimed by another Whitehall insider that the shock departure of Ms Mirza had encouraged No 10 to bring forward plans for the overhaul, which had been due to be unveiled next week.

Speculation grew that Mr Johnson could struggle to fill the vacant jobs. The Telegraph revealed this week that Antonia Romeo, one of Britain’s most senior female civil servants, had decided against applying for the newly-created Permanent Secretary role.

Amid Westminster intrigue about the Prime Minister’s leadership, Simon Clarke, the chief secretary to the Treasury, told Channel 4 News: “I think the last days of Rome were more fun.”

The resignation of Ms Mirza, who had worked with Mr Johnson since his City Hall days, was seen as a bruising loss. She criticised him over his “inappropriate and partisan” jibe at the Sir Keir earlier this week, when he accused the Labour leader of “failing to prosecute Jimmy Savile” during his time as Director of Public Prosecutions.

Mr Johnson at first doubled down on his comments despite a backlash, but backtracked in an interview on Thursday. While he disavowed the claim, he stopped short of an apology.