In the leaked documents, he called the Trump administration's policy toward Iran "incoherent", said the president might be indebted to "dodgy Russians" and raised doubts about whether the White House "will ever look competent".
By resigning, Sir Kim clearly wanted to put an end to an extraordinary chapter in the so-called special relationship. Darroch said in his resignation letter it had become "impossible" to do his job after diplomatic cables were leaked over the weekend.
In the Commons, Theresa May told MPs that she had spoken to Sir Kim and told him that it was a "matter of great regret" that he felt it necessary to leave his post.
"I told her how it should be done, but she chose to go another way", he started, before stating the United States would not have a relationship with the ambassador any longer. "I don't know what the motivations would be at this stage but it is very important that we find out who actually carried out this particularly damaging act".
Prime Minister Theresa May said Sir Kim had given "a lifetime of service" to the United Kingdom.
He went on, "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". Appointing ambassadors usually involves a formal civil service process with advertisements, applications and interviews, though Simon McDonald, head of Britain's diplomatic service, said the post of ambassador to the US wasn't always chosen that way.
Memos from Kim Darroch in which he described the Trump administration as inept were leaked to a British Sunday newspaper, infuriating the USA president, who launched a Twitter attack on both the envoy and outgoing British Prime Minister Theresa May, who had given Darroch her full support.More news: IndiGo share prices drop as promoters' battle comes to fore
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The choice of Darroch's replacement will be one of the first matters on the next prime minister's desk, Fletcher says.
Hunt, who is Britain's foreign secretary, vowed to keep Darroch in the post, but Johnson pointedly did not.
"The prime minister, foreign secretary and whole of the public service have stood with you: you were the target of a malicious leak; you were simply doing your job", McDonald added.
"Friends speak frankly so I will: these comments are disrespectful and wrong to our Prime Minister and my country".
He said he regretted how an "outrageous leak caused this".
"It's hard to describe just how big a blow to our diplomatic standing in the world this resignation represents", tweeted Tom Watson, the deputy leader of the opposition Labor party.
Trump concluded his tweets by demanding that someone tell Darroch "the U.S. now has the best Economy & Military anywhere in the World, by far and they are both only getting bigger, better and stronger.Thank you, Mr. President!"
"He has basically thrown this fantastic diplomat under the bus to serve his own personal interests", he told BBC TV.