Donald Trump’s explosive interview with The Sun could hardly have been designed to be more embarrassing for Theresa May.

On the very day when she sought to rally Conservative troops behind her plans for EU withdrawal, the US President threw his considerable weight behind those who accuse her of betraying Brexit.

And to make matters worse, he poured praise on the very man who is the biggest thorn in the Prime Minister’s side and who many expect eventually to challenge her for the job – former foreign secretary Boris Johnson.

A trade deal with the US is the jewel in the crown for supporters of Brexit, with improved access to massive American markets one of the most tangible possible benefits of leaving the EU.

For Mr Trump to suggest that Mrs May has “killed” any possibility of a deal – and that she could have done better if she had taken his advice – amounts to a comprehensive trashing of her record as Prime Minister.

When Mr Trump first took office last year, Downing Street was consumed by eagerness to ensure Mrs May was his first international visitor at the White House. The photographs showing them holding hands and Mrs May’s unexpected offer of a state visit to Britain showed the lengths she was willing to go to demonstrate the closeness of the trans-Atlantic “special relationship”.

How badly that has now backfired on Number 10.

The President’s deeply-embarrassing comments emerged moments after Mr Trump had been given a red-carpet welcome fit for a bosom friend at Blenheim Palace, and just as Mrs May made her speech declaring what a “joy” it was to stand side-by-side with the US.

Donald Trump visit to UK
US President Donald Trump and his wife Melania are welcomed by Prime Minister Theresa May and her husband Philip May at Blenheim Palace (Stefan Rousseau/PA)

Downing Street had apparently been warned that Mr Trump had done an interview with the UK’s biggest-selling tabloid newspaper, but had been assured its tone was positive.

His bombshell in the printed media can only have left Mrs May deeply apprehensive about what the President might say when standing alongside her in front of the world’s TV cameras following their talks at Chequers on Friday.

The Prime Minister prefers a tightly-controlled approach to press conferences, delivering carefully-scripted lines to drive home her core message.

As his performance at Nato showed on Thursday, Mr Trump takes the opposite approach, firing off scatter-gun, apparently off-the-cuff remarks in sometimes rambling responses which can surprise his hosts and his White House staff alike.

International visits like this week’s are normally heavily-choreographed affairs, with months of work going into ensuring that leaders have plenty of good news to announce and finessing any points of contention between them.

Above all, care is taken to avoid anything that could be regarded as offensive to your hosts, with the media picking over any tiny deviation from this rule in the search for possible “snubs”.

When Barack Obama came to London to give his support to David Cameron in the EU referendum, he sat down with the Prime Minister to discuss what he could say that would be most helpful to his cause.

Mrs May has learnt the hard way that this is not how Donald Trump works. Deliberately or not, he has added to her woes in one of the most difficult weeks of her premiership.

And she is left with the worry that the very man whose help she needs to deliver a dividend from Brexit may be actively conniving with those seeking to unseat her.