The inquiry into the leak of diplomatic cables criticising Donald Trump’s White House is focusing on whether “someone within the system” was responsible, a Foreign Office minister has said.

Sir Alan Duncan said there was no evidence the dispatches from Sir Kim Darroch – Britain’s ambassador to the US – had been obtained through computer hacking.

Instead, he said the investigation was looking at the possibility they had been “illicitly” released by someone with access to diplomatic reports.

Sir Kim announced on Wednesday he was standing down from his posting in Washington, saying his position had become “impossible” following a barrage of abuse from President Trump.

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Sir Kim Darroch said his position had become ‘impossible’ (Niall Carson/PA)

Downing Street has said “initial discussions” have taken place with the police who could become formally involved in the leak inquiry if there was evidence of “criminal activity”.

In the Commons, Sir Alan told MPs: “We do not, at the moment, have any evidence that this was a hack so our focus is on finding someone within the system who has released illicitly these communications… that is where the inquiry is primarily focused at the moment.”

There was continuing anger among many MPs at the role played by Boris Johnson, whose repeated refusal to back Sir Kim in Tuesday’s Tory leadership debate was widely seen to have contributed to his decision to quit.

The frontrunner to succeed Theresa May insisted it was nothing to do with him, saying he was “very surprised” at the construction which had been placed on events.

“I can’t believe they’re trying to blame me for this,” he told The Sun.

“It seems bizarre to me. I’m a great supporter of Kim’s. I worked very well with him for years. I think that he’s done a superb job.”

Sir Alan, who previously accused Mr Johnson of having thrown Sir Kim “under a bus”, said he hoped the the “entire apparatus of government” would ensure the ambassador was looked after following his departure from Washington.

“Sir Kim Darroch’s career is not over. I hope the House will appreciate that although this is a difficult moment, it doesn’t mean that’s the end of his career,” he told MPs.

“I hope the Foreign Office and the entire apparatus of government will look after him, appreciate his merits and make sure he can be redeployed somewhere else for the benefit of our United Kingdom.”

Meanwhile, Downing Street has refused to be drawn on whether Mrs May intends to appoint a new ambassador before she leaves office in two weeks’ time.

Allies of Mr Johnson have insisted that it must be for the next prime minister to decide who Britain’s new envoy to the US should be.

However in response to questions, Mrs May’s official spokesman said only: “In terms of this particular replacement, that will take place in due course.”

Sir Alan, however, hinted that an early appointment may be unlikely.

“We do really want to make sure we get the very best person and I think it’d be a pity if in the interests of alacrity we chose a number two rather than a number one,” he said.

“So it’s not for me to make any further comment on that really. I don’t know whose names might be in the frame, but that’s a matter for the Prime Minister to decide.”