The US president had branded him "a very stupid guy" after emails emerged where the ambassador had called his administration "clumsy and inept".

Theresa May said Sir Kim's departure was "a matter of deep regret".

He said he wanted to put an end to speculation about his role and the leak had made it "impossible" to continue.

In a letter to the Foreign Office, Sir Kim said: "Although my posting is not due to end until the end of this year, I believe in the current circumstances the responsible course is to allow the appointment of a new ambassador."

The leak was described as "malicious" by Sir Simon McDonald, permanent under secretary and head of the diplomatic service, who told Sir Kim: "You are the best of us."

Mrs May said he had had the full backing of the cabinet and had given a "lifetime of service" to the UK, for which he was owed an "enormous debt of gratitude".

"Good government depends on public servants being able to give full and frank advice", she said.

She spoke of the importance of "defending our values and principles particularly when they are under pressure".

His resignation has prompted widespread support for Sir Kim while some have questioned Tory frontrunner Boris Johnson's stance.

Mr Johnson had refused to say, during the Tory leadership debate on Tuesday night, whether he would keep Sir Kim in post if he became prime minister.

Following Sir Kim's resignation, he said he was "a superb diplomat" and whoever was responsible for the leak "has done a grave disservice to our civil servants".

Europe Minister Sir Alan Duncan said it was "contemptible negligence" not to support Sir Kim.

"He's basically thrown this fantastic diplomat under a bus to serve his own personal interests," he said.

Fellow Tory leadership candidate and Foreign Secretary Jeremy Hunt said he "profoundly" regretted the "outrageous" leak that led to Sir Kim's departure. "It should never have come to this", he added.

BBC political editor Laura Kuenssberg said: "Failing to back Darroch last night was the first major act of the still hypothetical Johnson premiership that led to his resignation."

In the Commons, Labour leader Jeremy Corbyn described Mr Trump's comments about him as "beyond unfair and wrong."

In the emails leaked to the Mail on Sunday, Sir Kim said: "We don't really believe this administration is going to become substantially more normal; less dysfunctional; less unpredictable; less faction-riven; less diplomatically clumsy and inept."

The emails, dating from 2017, said rumours of "infighting and chaos" in the White House were mostly true.

Sir Kim thanked those who had offered their support, both in the UK and the US during a "difficult few days", adding that it had "brought home to me the depth of friendship and close ties between our two countries".

The government has opened an internal inquiry into the publication of the memos.

Police have been urged to open a criminal investigation into the leak.

Who is Sir Kim Darroch?

Born in South Stanley, County Durham, in 1954, Sir Kim attended Durham University where he read zoology.

During a 42-year diplomatic career, he has specialised in national security issues and European Union policy.

In 2007, Sir Kim served in Brussels as the UK permanent representative to the EU.

He was the prime minister's national security adviser between 2012 and 2015, dealing with issues such as the rise of the Islamic State group in Iraq and Syria, Russian annexation of Crimea, the nuclear threat from Iran and the collapse of government authority in Libya.

He became ambassador to the US in January 2016, a year before Donald Trump's presidential inauguration.