Donald Trump has launched a renewed attack on the British ambassador and Theresa May, labelling them “very stupid” and “foolish” respectively.

The US president’s broadsides against the prime minister and Sir Kim Darroch came after leaked memos revealed the UK ambassador to Washington had branded the Trump White House “inept” and “dysfunctional”.

“The wacky Ambassador that the U.K. foisted upon the United States is not someone we are thrilled with, a very stupid guy,” Mr Trump tweeted on Tuesday morning. ”He should speak to his country, and Prime Minister May, about their failed Brexit negotiation, and not be upset with my criticism of how badly it was handled.”

“I told @theresa_may how to do that deal, but she went her own foolish way-was unable to get it done. A disaster! I don’t know the Ambassador but have been told he is a pompous fool.

“Tell him the USA 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!”

Mr Trump, who has the power to expel any foreign diplomat he wishes, had earlier announced the US would “no longer deal” with Sir Kim, who was “not liked or well thought of” within the country. He also criticised Ms May for the “mess” he claimed she had created over Brexit.

Ms May’s spokesperson said in response it is the UK government which “determines who its ambassador is”.

The escalating diplomatic crisis between the US and Britain was sparked when the Mail on Sunday obtained diplomatic memos from Sir Kim, who in them described the US administration as “uniquely dysfunctional” and questioned whether it “will ever look competent”.

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There is no suggestion Sir Kim was upset over Mr Trump’s criticism of the UK’s Brexit negotiation strategy with the European Union

In one scathing assessment, Sir Kim wrote: “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 top diplomat also suggested that in order to communicate with the US president “you need to make your points simple, even blunt”.

The Foreign Office, which on Sunday launched an investigation into the source of the leak, has been contacted for comment.

The publication of the cables, which the Foreign Office has confirmed as genuine, has created an embarrassing headache for the government.

The House of Commons Foreign Affairs Committee has launched an inquiry into the department's secure communications and handling of classified information in the wake of the disclosure of Sir Kim's memos.

In letters to Ms May, foreign secretary Jeremy Hunt and Metropolitan Police commissioner Cressida Dick, committee chair Tom Tugendhat voiced concern about a "culture of leaks" which he said was damaging the UK' s reputation, impacting on the government's ability to function and undermining relationships with close allies. Mr Tugendhat repeated his call for a police inquiry.

Ms May has said she has full confidence in Sir Kim, even while stressing that while it was the ambassador’s job to provide “an honest and unvarnished view” of the US administration, she was not necessarily required to agree with everything he wrote.

Sir Kim was not attending a meeting between Liam Fox, the international trade secretary, and the president’s daughter, Ivanka Trump, when Mr Fox planned to apologise for the way “that either our civil service, or elements of our political class, have not lived up to the expectations that either we have, or the United States has, about their behaviour”.

The job of ambassador to Washington is probably the most senior posting for a diplomat from the UK, or any other country. While the UK would normally seek to resist having its choice of envoy dictated to it, its hand is somewhat weakened by current circumstances.

Firstly, the government may have initially expected Mr Trump to brush aside the matter. On Sunday, he appeared to do so when he told reporters: “We’ve had our little ins and outs with a couple of countries and I would say that the UK, and the ambassador has not served the UK well, I can tell you that.”

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He added: “We’re not big fans of that man and he has not served the UK well, so I can understand it.”

On Monday, it was reported Sir Kim had been disinvited from a dinner that treasury secretary Steven Mnuchin was hosting with Mr Trump and the emir of Qatar.

The decision on whether to replace Sir Kim will not be that of Ms May’s for much longer. On 23 July the Conservatives will elect a new leader and in doing so appoint the next prime minister.

Polls show the former London mayor and foreign secretary Boris Johnson to be some way ahead of the current foreign secretary, Jeremy Hunt, in the two man showdown. Mr Trump, who has said he likes Mr Johnson and suggested he would make a good prime minister, has also said Nigel Farage, the leader of the Brexit Party, could be ambassador to Washington.

Mr Farage is among those who have called for Sir Kim to be sacked.