Boris Johnson has given his overhauled Cabinet a “half-time pep talk”, urging them to unite to deliver for the nation, after carrying out a ruthless cull in his top team.

In the first meeting of the new Cabinet on Friday, the Prime Minister said it is time to “spit out the orange peel” and work together, having sacked three people who would otherwise have joined them around the table in Downing Street.

Both demoted Justice Secretary Dominic Raab and his replacement as Foreign Secretary, Liz Truss, sat opposite Mr Johnson amid reports they have both staked a claim to the Chevening grace-and-favour residence.

Mr Johnson appeared to be in a buoyant mood, making jokes and deploying metaphors as he gave an opening speech to the ministers crowded around the Cabinet table, not wearing masks.

With former education secretary Gavin Williamson among those sacked, the Prime Minister told the surviving Cabinet members they are all there on “merit”, but he added it is time to redouble their efforts to deliver for the public.

“I’m just thinking about delivery… I’ve seen a few delivery rooms, probably seen as many delivery rooms as anybody in this… with the possible exception of Jacob (Rees-Mogg, the Commons Leader),” said Mr Johnson, a father of at least six.

“I know that delivery normally involves a superhuman effort by at least one person in the room.

“But there are plenty of other people in that room who are absolutely indispensable to that successful outcome.”

Mr Johnson’s wife Carrie is pregnant with their second child but he refuses to say how many children he already has, while Mr Rees-Mogg has six children.

The Prime Minister continued: “To mix my metaphors, this is, if you like, the half-time pep talk.

“This is the moment when we spit out the orange peel, we adjust our gum shields and our scrum caps.

“We get out on to the pitch in the knowledge that we’re going to have to do it together and we’re going to have to do it as a team.”

Cabinet reshuffle
Newly-appointed Foreign Secretary Liz Truss arrives in Downing Street for the first Cabinet meeting after the reshuffle (Stefan Rousseau/PA)

Along with Mr Williamson, the absentees were Robert Jenrick and Robert Buckland, who were dispatched to the backbenches having served as housing secretary and justice secretary.

Any reshuffle comes with tensions, and Downing Street has not denied reports that Mr Raab resisted his change of roles during a tense conversation with the Prime Minister.

Demoted following his handling of the Afghanistan crisis, Mr Raab was sat side-by-side with his successor around the Cabinet table in No 10 on Friday.

They were both facing Mr Johnson after it was reported the Prime Minister will have to decide which one to grant access to Chevening.

The Times said Mr Raab believes his new role of Deputy Prime Minister, which formalised a title he effectively held and was largely interpreted as a consolation prize, means he should be able to keep it, although by convention access is usually bestowed on the Foreign Secretary.

Downing Street said no decision would be made over which minister will get access to the Kent residence until the reshuffle is over, with a few lower ranking changes still to come.

“There is a long process in place for nominating the occupants of Chevening House and we will update in due course,” the Prime Minister’s official spokesman said.

“We will conclude the reshuffle and then we will get into the longstanding processes, like residences.”

He said there was not “one single post” that was entitled to use the Grade I listed building.

Presenting himself as head of a Government that can take on issues that have “bedevilled” other administrations, Mr Johnson pledged they would “get social care done” and would enable the NHS to “bounce back from the pandemic”.

Mr Johnson casting his discussion as a “half-time pep talk” will do nothing to dispel suspicions he was making tactical substitutions with the next general election in his mind.

Quickly after being repositioned as Tory party co-chairman, former culture secretary Oliver Dowden urged Conservative staff to get ready for the next poll, which could be in 20 months’ time.

Mr Johnson’s bloodletting continued into Thursday when some lengthy frontbench careers were ended at a stroke as he axed some from the lower ranks of the administration.

John Whittingdale – who had been serving as media minister – was the highest-profile casualty, while Nick Gibb’s lengthy tenure in the Department for Education was also brought to an end.

Mr Whittingdale said some changes were predictable while others “came out of the blue” as he recognised a need to make the Cabinet more representative of wider society.

“But equally I think it’s no bad thing to have a bit of experience around that table and people who have got a good grasp of the detail of the jobs that they’re being asked to do,” he told BBC Newscast.

Meanwhile, Mr Johnson sent David Duguid to the backbenches and appointed James Cartlidge as a replacement assistant whip.

George Freeman was made minister for science, research and innovation.

Tom Pursglove, Maria Caulfield and David Rutley were made parliamentary under secretaries of state.