Some in government hope new evidence from the continuing public inquiry into the Covid pandemic will provide a pretext to force his replacement. During hearings last year, it was suggested he had advocated mass exposure to the virus akin to “chicken-pox parties”.

Wormald, who was unexpectedly made cabinet secretary by Starmer last December, was permanent secretary at the Department of Health and Social Care during the pandemic.

He has already been criticised by one of the inquiry’s reports, which found there had been a “lack of adequate leadership” in preparations for Covid and said the civil service and governments “failed their citizens”, at the time of his appointment.

Reports over the summer suggested that No 10 was experiencing “buyer’s remorse” over Starmer’s choice of cabinet secretary.

His decision to appoint a career civil servant dogged by controversy to “rewire the state” left many in government mystified. Wormald’s father and grandfather both served in senior roles on Whitehall.

Dominic Cummings, the former adviser to Boris Johnson who worked alongside Wormald during the pandemic and at the Department for Education, told The Times last Saturday that the cabinet secretary was “part of the old broken system”.

He said: “The old system has shot themselves in both feet, they’ve blown both feet off with Starmer and Wormald, because they’ve made it conventional wisdom now that the old system is broken and has to be succeeded by something much more radical.”

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Senior advisers in Downing Street are sympathetic to that critique, but have found their room for manoeuvre constrained by an “unwritten rule”, which dictates that cabinet secretaries cannot be dismissed until they have spent a year in the post.

A No 10 insider said: “Chris is a parody of every civil service stereotype. He is given clear instructions on an issue and says we will be able to deliver it only after we’ve commissioned a wide-reaching review that reports sometime in the mid-2080s.”

The unease over Wormald’s effectiveness reflects longstanding concerns about Downing Street’s lack of grip on the machinery of government.

Over the summer, there were plans to circumvent him by appointing Casey, presently a non-executive director of the Cabinet Office, as permanent secretary of No 10, but the new role did not feature in Starmer’s shake-up of his inner team.

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Whitehall sources added that there was a “widespread assumption” that Starmer would “fire Chris Wormald” and replace him with Casey.

A Cabinet Office spokesman said: “The cabinet secretary continues to have the support of the prime minister and they are working closely together to deliver on the priorities of the British public.”