He also declined to back The Mail on Sunday’s decision to publish the diplomat’s top-secret communications, because there was an “ongoing investigation”.
The Met was forced to issue a second statement over the weekend after the furore which greeted its warning that publication of the cables could constitute a criminal offence.
Mr Johnson condemned the “chilling effect on public debate” – while Mr Hunt said: “I defend to the hilt the right of the press to publish those leaks.”
But, asked if Ms May had similar criticisms, her spokesman replied: “The Metropolitan Police has issued two statements and both are a matter for them. I won’t comment on either.”
Asked if she was committed to press freedom, he replied: “A free press is one of the foundations on which our democracy rests.”
Neil Basu, the Met’s assistant commissioner, triggered the storm late on Friday, when he criticised publication of the cables “now knowing they may be a breach of the OSA” [Official Secrets Act].
“The publication of leaked communications, knowing the damage they have caused or are likely to cause, may also be a criminal matter,” he said.
A later statement rowed back, by insisting “the focus of the investigation” was on the leaker, but continued to insist publication risked committing “a criminal offence”.
David Davis, the former Brexit secretary, called for Mr Basu to be stripped of his role in the investigation and replaced by an officer who puts a free press before “the state's reputation”.