The U.K. government said Monday leaks of memos in which its ambassador to the U.S. described President Donald Trump's administration as "dysfunctional" were a matter of regret, and promised to investigate.

The memos from Kim Darroch, the ambassador to Washington, were leaked to a Sunday newspaper, annoying Trump and triggering demands on the U.K. side to find out who had disclosed them.

"Contact has been made with the Trump administration setting out our view that we believe the leak is unacceptable. It is, of course, a matter of regret that this has happened," a spokesperson for Prime Minister Theresa May told reporters.

Trump tweeted later on Monday that he "will no longer deal" with Darroch. "I do not know the Ambassador, but he is not liked or well thought of within the U.S.," Trump said in a pair of tweets that also took aim at how May handled Brexit.

"The good news for the wonderful United Kingdom is that they will soon have a new Prime Minister."

The leaked cables were intended for senior U.K. ministers and civil servants, and officials believe the mole will be found among politicians or officials from Britain, rather than overseas.

"I've seen nothing to suggest hostile state actors were involved," said May's spokesperson, James Slack.

The inquiry is being led by civil servants in the Cabinet Office, and Slack said police would only be called in "if evidence of criminality is found."

It's possible the person behind the leak could be charged with breaching the Official Secrets Act, which bars public servants from making "damaging" disclosures of classified material. Breaching the act carries a maximum sentence of two years in prison, though prosecutions are rare.

'It is, of course, a matter of regret that this has happened,' a spokesperson for Theresa May told reporters about the memo leak involving Trump, shown here with the U.K. prime minister in London last month. (Carlos Barria/Reuters)

Foreign Secretary Jeremy Hunt told reporters Monday he did not share the ambassador's assessment of either the U.S. administration or relations with it, but defended Darroch's "right to make that frank assessment," saying the ability to communicate frankly was "fundamental" to diplomacy.

He promised there would be "very serious consequences" if the culprit gets caught.

'Full faith' in diplomat

Slack said May had "full faith" in Darroch, a long-serving diplomat, although she too didn't agree with his characterization of the Trump administration.

He said ambassadors were hired to provide "honest, unvarnished assessments" of politics in the countries where they served, which didn't necessarily reflect the views of the government.

U.K. Trade Secretary Liam Fox, who is on a visit to Washington, told BBC Radio he would apologize for the leak to Ivanka Trump, the president's daughter. Fox is due to meet her during his trip.

"I will be apologizing for the fact 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, which in this particular case has lapsed in a most extraordinary and unacceptable way," Fox said.

"Malicious leaks of this nature ... can actually lead to a damage to that relationship, which can therefore affect our wider security interest."

The revelations come at a time when the U.K. is hoping to strike a major trade deal with its closest ally after it leaves the European Union, an exit scheduled for Oct. 31.

Trump told reporters, of Darroch: "We are not big fans of that man and he has not served the U.K. well, so I can understand and I can say things about him, but I won't bother."

'Clumsy and inept'

In memos to his government dating from 2017 to the present, Darroch said reports of in-fighting in the White House were "mostly true," and last month described confusion within the administration over Trump's decision to call off a military strike on Iran.

"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," Darroch wrote in one memo.

Nigel Farage, leader of the Brexit Party and long a thorn in the side of British governments, said figures such as Darroch would "not be around" if ex-foreign minister Boris Johnson, one of two candidates seeking to replace May as prime minister, was chosen by Conservative Party members.

Despite being close to Trump, Farage ruled himself out of becoming Britain's next ambassador in Washington.

"I don't think I'm the right man for that job," Farage told BBC Radio.

It's the second serious disclosure of confidential material this year.

Two months ago, May fired Gavin Williamson as defence minister after secret discussions in the National Security Council about Chinese telecom firm Huawei were leaked to the media, and an inquiry concluded he was responsible.

Williamson denied any involvement and police said there was no reason for a criminal investigation.