Kim Darroch quit on Wednesday after Donald Trump called him "stupid" and "wacky" following the publication of the confidential memos by a newspaper. In them, Darroch called Trump's administration inept.
"Given the widely reported consequences of that leak I am satisfied that there has been damage caused to UK international relations, and there would be clear public interest in bringing the person or people responsible to justice," Metropolitan Police Assistant Commissioner Neil Basu said in a statement.
"I would say to the person or people who did this, the impact of what you have done is obvious. However, you are now also responsible for diverting busy detectives from undertaking their core mission. You can stop this now. Turn yourself in at the earliest opportunity, explain yourself and face the consequences."