A Cabinet war over the appointment of a new ambassador to the US has escalated, as one ally of Boris Johnson accused Theresa May of being “in denial” over the fact she must soon give up the reins of power.

The prime minister is coming under intense pressure to leave the choice of a replacement for Sir Kim Darroch to her likely successor, who is thought to be keen to parachute in a pro-Trump, pro-Brexit envoy who can smooth the way to a US trade deal.

But Downing Street has not ruled out an appointment during Ms May’s final two weeks in office before she steps down on 24 July.

And one Johnson-backing cabinet minister said that the PM had been doggedly sticking to a “business as usual” approach since announcing her resignation plans on 24 May, continuing to make decisions which will have their long after she has left power.

“She does seem to be in denial,” said the minister. “At the first Cabinet meeting after she announced her resignation she didn't even refer to it.

“She just keeps going with business as usual, talking about what needs to happen in October, when she won’t even be here in October. We just keep having meetings and no-one is quite sure why.”

The minister added: “It might be a bit of a shock in a fortnight when she's out and Boris is in charge.”

Sir Mark Sedwill is being tipped for the Washington ambassador's job (AFP/Getty Images)

Speculation is rife in Westminster over the identity of the successor to Darroch, who dramatically quit on Wednesday after coming under fierce attack from Mr Trump over disparaging comments in diplomatic memos about the “inept” president.

Names in the frame include current cabinet secretary and national security adviser Sir Mark Sedwill, in what might be seen as a reward for loyal service to Ms May, or current ambassador to the UN Karen Pierce, who would be the first woman to take the plum post in Washington.

It is thought Mr Johnson may prefer a more political figure, with the names of former chancellor George Osborne and international trade secretary Liam Fox - or even Brexit Party leader Nigel Farage - being bandied around. Mr Farage himself has said he is "not the right man for the job", though he suggested he "could be very useful" in building links with the Turmp White House.

Nigel Farage said he "could be very useful" in establishing closer links with the Trump team (EPA)

The Johnson-backing chair of the Commons Defence Committee, Julian Lewis, has expressed concern there could be “temptation for an outgoing prime minister to appoint to a plum job one of her inner circle”.

Downing Street declined to say whether Ms May would seek to appoint a new ambassador before stepping down, saying only that Sir Kim's successor would be chosen "in due course".

"The ambassador is appointed by the prime minister on the recommendation of the foreign secretary, with the approval of the Queen," said Ms May's official spokesman.

"In terms of this particular replacement, that will take place in due course."