There has been speculation that Mr Sunak could pursue a job in venture capital or artificial intelligence, possibly in the US, were he to leave politics.

The Prime Minister used to live in California, where he attended Stanford business school and met his wife, Akshata Murty. The couple are understood to still own a home in California.

But asked on ITV’s Loose Women earlier this month whether he enjoyed his parliamentary duties enough to stay on as an MP regardless of Tory fortunes, he replied: “Gosh, I love being an MP. Yes, of course I’m staying. I love being an MP, I love my constituents, I love my home in North Yorkshire – it’s wonderful.”

Responding to the latest attack, the Prime Minister said: “I’m surprised that Lord Goldsmith who I don’t think I’ve spoken to in a very long time seems to have some sort of intimate knowledge of my family’s arrangements.”

Asked if he would leave for California, Mr Sunak said: “Of course not, my kids are at school, this is my home and as I said earlier my football team just got promoted to the Premier League so I intend to spend many more happy days watching them at St Mary’s.

“I was born and brought up in Southampton, I was raised with a very strong ethic of service to one’s community, that’s what I believe, that’s what I’ve always done.”

Pressed on whether he would do a full five years as an MP, he replied: “That’s what I’m here to do.”

Constituency-level polling last month suggested the Conservatives were on track for their heaviest defeat in history, although the first polls since Mr Sunak triggered the snap election indicated that there had been a slight increase in Tory support and favourability towards him among those who had backed Mr Johnson.

Lord Goldsmith quit Mr Sunak’s front bench in June last year after he was asked to apologise for criticising the privileges committee during its investigation into Mr Johnson over partygate.

The peer said at the time he was “able to get so much done previously” but had struggled to “hold the line” since Mr Sunak took office the previous year.

“The problem is not that the Government is hostile to the environment, it is that you, our Prime Minister, are simply uninterested,” he said. “That signal, or lack of it, has trickled down through Whitehall and caused a kind of paralysis.”

In response, Mr Sunak said he had asked Lord Goldsmith to apologise for his alleged role in putting pressure on the privileges committee, having shared a post calling it a “witch hunt” against Mr Johnson, only for the peer to “take a different course”.

Months later, Lord Goldsmith said he could be “very tempted” to back Labour at the next election as he attacked his party over its attitude towards the environment.

Mr Sunak has taken a more pragmatic approach towards net zero and climate change than Mr Johnson, delaying and diluting a number of green objectives as part of a reset of his leadership last summer.