DONALD Trump yesterday denied that he’d criticised Theresa May, despite an on-the-record interview with The Sun in which he openly criticised the Prime Minister.

There was fury in Whitehall over the article when it appeared late on Thursday night.

The president told the tabloid that he thought Boris Johnson would make a good Prime Minister, and that May’s new Brexit plan could “kill” any UK-US trade deal.

In an extraordinary press conference on Friday afternoon at Chequers, Trump initially appeared to say the interview, which was taped, was “fake news” before then admitting that he’d said everything he’d been quoted as saying, before admitting that he hadn’t read past the headlines.

He then told the press that he’d apologised to May, but that she’d replied: “Don’t worry it’s only the press.”

An apology from Trump is rare, if not unheard of.

In his interview, the commander-in-chief said he would have carried out the Brexit negotiations “much differently” and claimed the Prime Minister did not listen to his advice.

He told the paper: “If they do a deal like that, we would be dealing with the European Union instead of dealing with the UK, so it will probably kill the deal.

“If they do that, then their trade deal with the US will probably not be made.”

He went on to say Johnson, who quit as Foreign Secretary over the Chequers plan, was “a great representative for your country”.

Asked if he could become Prime Minister he added: “Well I am not pitting one against the other. I am just saying I think he would be a great Prime Minister. I think he’s got what it takes.”

When asked about the interview at the press conference, Trump said The Sun story missed out his positive comments about May.

He also promised to release a recording of the interview so people could hear all the “nice things” he said about May.

Trump also said he believed it was possible to do a trade deal with the UK after Brexit.

He said: “The only thing I ask of Theresa is that we make sure we can trade and we don’t have any restrictions because we want to trade with the UK and the UK wants to trade with us.

“We are by far their biggest trading partner and we have just a tremendous opportunity to double, triple, quadruple that.

“So if they go in a slightly different route – and I know they do want independence, it’s going to be independence, it’s just your definition – if they are going to go in a certain route I just said that I hope you are going to be able to trade with the United States.

“I read reports where that won’t be possible, but I believe after speaking with the Prime Minister’s people and representatives and trade experts it will absolutely be possible.”

Asked at the conference if he still thought Johnson would be a “great Prime Minister,” Trump replied: “He’s been very nice to me. He’s been saying very good things about me as president.

“I think he thinks I’m doing a great job. I am doing a great job, I can tell you, just in case you haven’t noticed.

“Boris Johnson, I think, would be a great Prime Minister.”

Trump added: “I also said that this incredible woman right here is doing a fantastic job, a great job.

“I mean that. And I must say, I have gotten to know Theresa May much better over the last two days than I have known her over the last year-and-a-half. I think she’s a terrific woman. I think she’s doing a terrific job. And, that Brexit is a very tough situation, that’s a tough deal.

“She’s going to do the best.”

Trump was also pressed on his claim that immigration had damaged the cultural fabric of Europe.

The president then linked terrorism to immigration: “I think it has been very bad for Europe. Europe is a place I know very well and I think that what has happened is very tough. It’s a very tough situation. I mean, you see the same terror attacks that I do. We see them a lot.”

After the press conference, Trump and First Lady Melania, met the Queen at Windsor castle.

He then filmed an interview with his close personal friend Piers Morgan before Air Force One flew into Prestwick Airport. He will spend the next two days at his Turnberry course.