Party chairman Richard Holden has also quit. The Independent has been told angry Tories began texting him at 4am on Friday demanding his resignation.

Lord Cameron has stepped back from frontline politics after last week’s election defeat but will keep his House of Lords seat for life.

He was given a peerage last November so that Rishi Sunak could make him his foreign secretary.

But the ex-PM has tendered his resignation and will not serve in the shadow cabinet now the party is out of government.

Also quitting is party chairman Richard Holden, blamed by many for the depth of his party’s defeat.

He has faced accusations that he “stitched up” a safe seat for himself when he should have been saving other MPs, a charge he denies.

The Independent has been told that Tory MPs started texting Mr Holden at 4am on Friday morning asking why he had yet to tender his resignation.

Rishi Sunak will remain the leader of the Conservatives’ interim shadow cabinet until his replacement is appointed.

He quit last week in the wake of the result.

The party has named Jeremy Hunt, who narrowly held his seat on Thursday, its shadow chancellor, with James Cleverly shadow home secretary, mirroring the portfolios they held in government.

Former deputy foreign secretary Andrew Mitchell will become the shadow foreign secretary, while Richard Fuller, the former economic secretary to the Treasury, has been made the new Conservative chairman.

Leadership frontrunner Kemi Badenoch has been shifted to become shadow levelling-up secretary, while Kevin Hollinrake will shadow her former Business Secretary post.

He went on to pick out businesses in the food and drink sector, particularly small and medium-sized enterprises.

Remarkably, asked about his comments, Mr Sunak agreed saying: “Of course when you leave the single market and the customs union that is going to change our trading relationships.”

Mr Fuller said in a statement: “The Conservative Party has had a difficult election and it is important that we regroup and reflect on these results. We should also challenge ourselves candidly and deeply on the strengths of the Conservative Party across the country and outline where improvements can be made.

“I am honoured to be asked to act as interim chairman of the Conservative Party and to be working alongside colleagues in the shadow cabinet.

“United as a party we will be ready and able to hold this new Labour government to account every step of the way.”

The Tories won just 121 seats last Thursday, their worst result in the party’s 190-year history, as millions of their voters switched to Labour, the Lib Dems, Nigel Farage’s Reform or didnot vote at all.

On Monday Mr Hollinrake suggested any leadership race could drag on until the end of the year, adding that “I don’t think there is any rush”.