Face of Nation : The PM’s spokesman added that the leak was “absolutely unacceptable” and No 10 had made contact with the White House.
Sir Kim Darroch, the UK’s ambassador in Washington, described Donald Trump’s administration as “inept” in emails.
A senior Conservative MP has asked the Metropolitan Police to open a criminal investigation into the leak.
The US president responded to Sir Kim’s comments by saying “we’re not big fans of that man and he has not served the UK well”.
The prime minister’s spokesman said it was “the job of ambassadors to provide honest and unvarnished opinions” but Mrs May “does not agree with the assessment”.
“The leak is absolutely unacceptable and, as you would expect, contact has been made with the Trump administration setting out our view that we believe that it is unacceptable,” he added.
The chairman of the foreign affairs committee, Tom Tugendhat, told the House of Commons on Monday he had written to Met Commissioner Cressida Dick to ask for a criminal investigation.
“I have asked her for reassurance that all necessary resources will be made available to ensure that the source of this leak is determined as a priority,” he said.
Foreign Office minister Sir Alan Duncan responded by saying a cross-government investigation would be “comprehensive” and the police “could be involved” if there was evidence of criminality.
Trade secretary Liam Fox told the BBC the leak was “unprofessional, unethical and unpatriotic”, adding that whoever released the emails had “maliciously” undermined the defence and security relationship with the US.
“I hope if we can identify the individual, either the full force of internal discipline – or if necessary the law – will be brought to bear because this sort of behaviour has no place in public life,” he said.
But Labour’s shadow foreign secretary Emily Thornberry said Sir Kim had been “betrayed” and “hung out to dry even though his only crime was to tell the truth”.
She added: “He told the truth about Donald Trump and that was because it was his job.”
Just imagine if every heavily encrypted report to Whitehall from all UK ambassadors overseas was instantly available on your mobile.
The candour would cease immediately and they’d become ultra-bland and useless as a tool in policy-making.
As the Foreign Office launched an investigation into the source of the leak to the Mail on Sunday, Mr Trump told reporters in New Jersey: “We’re not big fans of that man and he has not served the UK well.
“So I can understand it and I can say things about him but I won’t bother.”
In the emails, the UK ambassador to Washington said: “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.”
Sir Kim questioned whether this White House “will ever look competent” but also warned the US president should not be written off.
So, damage in this case is considerable. There will be a large number of potential suspects.
Diplomatic telegrams are seen by scores, often hundreds of people – ministers and officials – across several departments. That is to ensure grown-up and private conversations can be had based on large amounts of source material.
Of course, there is damage to relations between the UK and the Trump White House too.
Mr Trump likes to dish out insults and criticism (remember his frequent belittling of Theresa May over Brexit, and his all out verbal attacks on the mayor of London) but he is pretty thin-skinned when the verbal arrows are aimed at him.
The one person who is not under suspicion in London is Sir Kim himself. After all, as his current political master, Mr Hunt, has made clear, he was just doing his job.
