The London police said on Friday they have launched an investigation into the alleged leaks of the official memos that led to the resignation of the British ambassador to Washington.
The backlash comes after Scotland Yard launched an investigation into the leaking of confidential communications between the UK's ambassador to the US Kim Darroch, and the Foreign Office, in which he made disparaging remarks about the Trump administration.
The head of Britain's diplomatic service, Simon McDonald, said this week he was "bracing" himself for further leaks, which he described as "the worst breach of trust in our service in my career".
"The publication of leaked communications, knowing the damage they have caused or are likely to cause, may also be a criminal matter", said Mr Basu.
The British police has also advised "all owners, editors and publishers of social and mainstream media" not to publish leaked government documents, whether they already have them or are offered to publish new ones.
"The state threatening media freedom is a unsafe road to tread", Health Minister Matt Hancock said on Twitter.George Osborne, editor of the London Evening Standard and a former finance minister, described the remarks as a "very stupid and ill-advised statement from a junior officer who doesn't appear to understand much about press freedom".
"Going after the leaker is fair game, going after the media is not", he said.
The inquiry will be carried out by the Metropolitan Police counter terrorism command which is responsible for investigating breaches of the Official Secrets Act.
"If (journalists) are receiving stolen material they should give it back to their rightful owner and they should also be aware of the huge damage that's already been done and the potentially even greater damage that could be done", former defence minister Michael Fallon told BBC radio. You can stop this now.
Those comments drew a furious response from the president who denounced him as a "very stupid guy" and a "pompous fool" and said the the White House would no longer deal with him.
He said he had not defended the ambassador more because he did not think civil servants should be dragged into political disputes.
"He said that what somebody had relayed to him had been a factor in his resignation", Mr Johnson said. "Turn yourself in at the earliest opportunity, explain yourself and face the consequences".
Donald Trump reacted angrily on Twitter and cut ties with the British ambassador.
Asked in Friday's interview if he would be "as craven" a prime minister as he has been a candidate, Johnson said: "We have been very forthright with the United States of America and I will continue to be forthright".
Some senior Conservative figures criticised Mr Johnson over his perceived failure to defend Sir Kim.