In the leaked cables, Kim Darroch allegedly called Trump "inept" and "uniquely dysfunctional," according to a report from the Daily Mail published Sunday.
Ambassador Darroch announced his resignation after Trump dialed up his criticism of the diplomat on Tuesday, calling him "wacky" and "a very stupid guy."
In a letter to the U.K. Foreign Office announcing his resignation, Darroch said that the "current situation is making it impossible for me to carry out my role."
"Since the leak of official documents from this Embassy there has been a great deal of speculation surrounding my position and the duration of my remaining term as ambassador," he wrote. "I want to put an end to that speculation. The current situation is making it impossible for me to carry out my role as I would like. 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."
In response to Darroch's letter, Sir Simon McDonald, Permanent Under Secretary at the Foreign and Commonwealth Office, said the former Ambassador had been the target of a "malicious leak."
"I want to stress my deep appreciation for all you have done over the last four decades," he wrote. "In a series of demanding roles - including National Security Adviser and Permanent Representative to the European Union - you have loyally served the government of the day without fear or favour. We have been lucky to have you as a friend and colleague. You are the best of us."
Darroch had been dis-invited from a dinner Monday night with the president at the Treasury Department in honor of the emir of Qatar, according to a U.S. official. White House officials said this is an example of the kind of treatment Darroch will likely receive in the aftermath of the leak.
Prior to his resignation, a spokesperson for Prime Minister Theresa May's said that Darroch retained the government's "full support."
May told the U.K. Parliament that she had spoken with Darroch Wednesday morning, and his resignation was a matter of "deep regret."
"I told him that it is a matter of deep regret the he felt it necessary to resign his position as ambassador to Washington," she said. May also seemed to give an implicit criticism of President Trump, referring to the importance of "defending out values and principles, particularly when they are under pressure."
Alan Duncan, a minister for the Foreign Office, told Sky News that Johnson had "thrown him under the bus" and that he was "absolutely livid."
Jeremy Hunt, the current Foreign Secretary and Johnson's rival contender in the race to become the next prime minister, said that he was "deeply saddened" to hear of Darroch's resignation.
"Deeply saddened to hear of the resignation of Sir Kim Darroch," Hunt posted in a tweet. "Standing up for Britain means standing up for the finest diplomats on the world. It should never have come to this."