Kim Darroch resigned on Wednesday after a scandal with leaked diplomatic cables that contained unvarnished assessments of the USA administration, according to media reports.
He asked the person behind the leaks to turn themselves in and avoid wasting detectives' time, saying: "You can stop this now".
Britain's most senior counter-terrorism officer, Neil Basu, said on Friday police would investigate who was responsible but also warned journalists and publishers they too could be in breach of the law if further documents were leaked.
Scotland Yard's assistant commissioner Neil Basu released a statement urging the press not to publish leaked documents and to instead hand them to police.
He urged the culprits: "turn yourself in at the earliest opportunity, explain yourself and face the consequences".
His comments drew a furious response from the president who denounced him as a "very stupid guy" and a "pompous fool" and said the White House would no longer deal with him.
Mr Basu said in his statement: 'I would advise all owners, editors and publishers of social and mainstream media not to publish leaked government documents that may already be in their possession, or which may be offered to them, and to turn them over to the police or give them back to their rightful owner, Her Majesty's Government'.
Shortly afterwards Sir Kim announced his resignation saying "the current situation is making it impossible for me to carry out my role".More news: Picturesque Lake Popular on Instagram is Actually a Chemical Waste Dump
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Johnson himself acknowledged his comments had been partly responsible but denied he was to blame.
"They should also be aware of the huge damage that has already been done and the potentially even greater damage to be done by further breaches of the Official Secrets Act".
He said he had not defended the ambassador more because he did not think civil servants should be dragged into political disputes.
"Some people just told me. he actually said very good things about me", Trump said.
Sir Kim's resignation prompted widespread support for him - as well as criticism of Tory leadership frontrunner Mr Johnson.
Some Tories said Mr Johnson had thrown Sir Kim "under the bus" when he failed to give the ambassador his support in a TV debate after Mr Trump launched a war of words against the envoy. I do not know the ambassador, but he is not liked or well thought of within the US.
"But they've got to stop their leaking problems there, just like they have to stop them in our country".