Downing Street has said it is not focused on “tick-box diversity” after a reshuffle left the four great offices of state held by privately-educated men for the first time since the Tories’ 2010 election win.

The Cabinet shake-up is about forming a “strong and united team”, No 10 said as it defended the changes from questions about the lack of women in the most senior positions in Government.

Former prime minister Lord Cameron has been appointed Foreign Secretary while his predecessor James Cleverly has taken over from Suella Braverman as Home Secretary, with Jeremy Hunt remaining as Chancellor.

Answering questions about the reshuffle from reporters on Monday, Prime Minister Rishi Sunak’s press secretary said: “The Deputy Prime Minister (Oliver Dowden) went to a state school.

“This is about having a strong and united team that’s focused on delivering for the public and bringing in some of that experience, with David Cameron on the foreign policy brief to deliver the best for the country.

“That’s what we’re focused on rather than tick-box diversity.”

She said that women were getting senior jobs elsewhere in Government, adding: “You will see a lot of women rising up the ranks today.”

Three of the current office-holders – Mr Sunak, Mr Hunt and Lord Cameron – graduated with first class honours in philosophy, politics and economics (PPE) from the University of Oxford.

All four were educated at either public or private school, while two – Mr Sunak, who has Indian heritage, and Mr Cleverly, who has West African heritage – are from minority ethnic backgrounds.

Only eight women have ever served in one of the roles – Margaret Thatcher as prime minister, Margaret Beckett as foreign secretary, Jacqui Smith as home secretary, Theresa May as both home secretary and PM, Amber Rudd as home secretary followed by Priti Patel and Ms Braverman and Liz Truss as foreign secretary and PM.

No woman has yet held the role of chancellor.

The Truss ministry was notable for initially having no white men serving in the great offices of state for the first time in British political history, with Kwasi Kwarteng becoming the first black chancellor.