Donald Trump has said Britain’s ambassador to the US has “not served the UK well” as he hit back following the leak of confidential internal memos that presented an unflattering portrait of the president and his administration.

Earlier, the Foreign Office ordered an inquiry into the leaking of the cables, written by the ambassador, Kim Darroch, in which Trump’s White House is described as “uniquely dysfunctional” and “inept”.

Darroch said in the memos that media reports about vicious administration rows (“knife fights”, as he put it) were mostly true. He cast doubt on whether the Trump regime would ever become more stable, described the president as insecure, and suggested Trump’s career might end in disgrace.

Asked about the controversy in New Jersey by reporters on Sunday night, Trump said: “The ambassador has not served the UK well, I can tell you that. We are not big fans of that man … I can say things about him, but I won’t bother.”

Darroch’s comments were made in a series of briefings sent to London over the past two years, which were published by the Mail on Sunday. Although Darroch’s assessments are in line with a lot of mainstream commentary on the Trump regime, the publication of such remarks from the UK’s top diplomatic representative in the US is an embarrassment.

Commenting on the leak, the British foreign secretary, Jeremy Hunt, said: “This was a personal view. It’s not the view of the British government. It’s not my view. We continue to think that under President Trump the US administration is not just highly effective, but the best possible friend of the United Kingdom on the international stage.”

David Gauke, the justice secretary, told the BBC it was important for ambassadors to be able to give “honest, unvarnished advice” to ministers, and he said the leak of the cache of memos was “disgraceful”.

Tom Tugendhat, the Conservative chair of the Commons foreign affairs committee, told BBC Radio 4’s World This Weekend it was “a very serious breach” of diplomatic rules and that an inquiry must follow. “Diplomats must be able to communicate securely with their governments in order to be able to convey the messages that everybody needs to know,” he said. “Governments cannot make reasonable decisions unless they have all the facts available to them, and that means an honest assessment of the political situation in the host country.

“This must be investigated. And, if anybody is found to have been responsible, they must be prosecuted. This is a serious breach of trust between the British people and their employee, the person who leaked [the information].”

The Foreign Office said: “A formal leak investigation will now be initiated.”

Nigel Farage, leader of the Brexit party, said the leaked material showed why Darroch should be replaced as ambassador to the US. “From the moment Trump was elected, this man was the wrong person to be the British ambassador – a globalist in outlook, totally opposed to the Trump doctrine,” Farage said.

Darroch is due to leave his post at the end of this year, but the leak may encourage the next prime minister to appoint a successor more quickly. Mark Sedwill, the cabinet secretary, and George Osborne, the Tory former chancellor who now edits the Evening Standard, have been named in the media as potential candidates for the post. Trump once suggested that Farage himself should be put in charge of the Washington embassy.

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The Mail on Sunday scoop was written by Isabel Oakeshott, the journalist who ghost-wrote The Bad Boys of Brexit, an insider account of Farage’s role in the 2016 EU referendum. On Sunday she posted a message on Twitter dismissing claims that the leaks were influenced by a hidden agenda.

“Enjoying the conspiracy theories,” she wrote. “Isn’t it much simpler? In the absence of government, the civil service becomes politicised.”

In one of the most recent of the leaked memos, Darroch referred to “incoherent, chaotic” US policy on Iran and questioned Trump’s claim that he had called off a retaliatory air strike against Tehran after the downing of an American drone because he had heard at the last minute that 150 casualties were predicted.

Darroch said the claim “doesn’t stand up” because Trump would have been given the likely casualty figure in his initial briefing. Darroch said it was more probable that Trump had just changed his mind.

The US state department declined to comment.