Trump has always been a supporter of Brexit and has expressed enthusiasm for a wide-ranging trade deal with Britain after it leaves the European Union, something heralded by Brexit supporters as being one of the great benefits of exiting the bloc.
"If they do a deal like that, we would be dealing with the European Union instead of dealing with the United Kingdom, so it will probably kill the deal", Trump told the paper.
As he began a four-day visit to Britain on Thursday, Trump, a major supporter of Brexit, told The Sun that he had advised May to go about leaving the European Union in a different way but was ignored. One protest group has been given permission for a balloon in the president's image, shaded in orange and dressed in a diaper, known as the "Trump Baby Blimp", to hover over Parliament Square Garden.
Prime Minister May said they had discussed plans for an "ambitious" trade agreement.
The president started the day by reviewing a private military exercise alongside May at the Royal Military Academy Sandhurst.
And, although he insisted he was not trying to pit Johnson against May, he added: "I am just saying I think he would be a great prime minister".
A high metal fence has been erected around the US ambassador's central London residence where Trump will spend Thursday night and the embassy has sent out an alert warning Americans in London to keep a low profile in case protests turn violent.
Queen Elizabeth II is scheduled to host the president and first lady for tea at Windsor.
It added: "It was the latest global incident to erupt during Trump's brief sojourn overseas, which kicked off with incendiary comments that upended a North Atlantic Treaty Organisation summit in Brussels and further strained relationships with longtime United States allies".
"I think allowing millions and millions of people to come into Europe is very, very sad", the president said.
The comments, made in an interview with tabloid newspaper The Sun, were published Thursday night, just as Trump and May were wrapping up dinner after a red-carpet reception at Blenheim Palace, Oxfordshire.
He said he had gotten to know her a lot better in the last few days and reckoned she was a "tough negotiator and a very smart and determined person" who would do very well.
After a tumultuous couple years for the "special relationship" between the US and her closet ally, tested repeatedly by disagreements, the frustration at the street level with Mr. Trump's policies, style and manner manifested Thursday in some demonstrations.
Humiliating", added Labour MP for Exeter Ben Bradshaw.ADVERTISEMENTAnother Labour MP, Rupa Huq, told The Guardian that Trump's comments about Khanm, London's first Muslim mayor, constituted Islamophobia."A dash of Islamophobia lobbed at Sadiq Khan who he blames for terrorism. The president claimed Europe is "losing its culture" because of immigration from the Middle East and Africa. Trump said Khan had done "a bad job" on terrorism and crime in the capital.
"Paris, Nice, Brussels, Berlin. Cities in America all suffered terror attacks", Khan told British broadcaster Sky News.
In a near replay of their famous hand-holding at the White House, the president briefly took Mrs May's hand after arriving as they went up the stairs into the palace following a performance from a military band.
Outside the mansion, northwest of London, a couple of thousand booing demonstrators lined the road.