The pictures went around the world as a sign of the ‘extra-special relationship’ between Theresa May and Donald Trump – shots of the pair holding hands at the White House.

But yesterday a much less tender explanation emerged for the encounter – that he was clinging on to Mrs May for support because he has a morbid fear of stairs and slopes.

As Mrs May continued to bask in the success of her visit to the White House, a senior source suggested that the President suffers from a condition known technically as bathmophobia.

Gripping encounter: The President and Mrs May at the White House on Friday. One explanation indicates he has a fear of slopes and stairs

Mr Trump has already publicly admitted to being a ‘germaphobe’ with a compulsive need for cleanliness.

The source said: ‘He hates heights where you can see the ground or sharp inclines even more than germs. He particularly dislikes staircases and his biggest nightmare of all is a dirty stair rail.’

A number 10 spokeswoman said the hand was offered as a chivalrous gesture to Mrs May as they headed down a slope

They added that he did not have a problem at Trump Tower because ‘he is always in that gold elevator’. But even that is not without its risks for the tycoon: he reportedly will not press a ground-floor lift button because it is the most frequently touched and therefore riddled with germs.

Trump once said about handshakes: ‘One of the curses of American society is the simple act of shaking hands and the more successful and famous one becomes, the worse this terrible custom seems to get. I happen to be a clean-hands freak. I feel much better after I thoroughly wash my hands, which I do as much as possible.’

But the notoriously thin-skinned Mr Trump is unlikely to welcome the idea that he had to clutch Mrs May for support – especially as he has been plagued by jokes about the size of his hands.

Donald Trump has previously spoken about his phobia of germs and has said the practice of shaking hands is a 'curse'

A source close to the White House cast doubt on the claim saying he hadn't seen the new president struggle down slopes

Trump is reportedly so angry about one New York journalist’s jibe that he was a ‘short-fingered vulgarian’ that 30 years on from the claim he still sends the writer photos of himself, his hands outlined in gold marker pen to prove they are normal.

When asked about the hand-holding, a No 10 spokeswoman said that after a ‘very friendly’ meeting in the Oval Office, he ‘offered his hand’ as a ‘chivalrous gesture’ because they were about to walk down an unseen ramp.

A source close to the White House last night cast doubt on the bathmophobia claim, saying he had never noticed Mr Trump struggle with stairs or slopes. He also said there was no mention of the condition on the President’s public medical reports.