Just hours before Trump's interview was published, May invoked Winston Churchill, a hero of Trump, as she addressed the U.S. president and business leaders at a black-tie dinner at Blenheim Palace, the grand 18th-century country house that was the birthplace of the British World War Two leader.
It speculated that Mr Trump may have been "wound up" over Brexit by British politician Nigel Farage, the former UK Independence Party leader who campaigned for years for Britain to leave the European Union, or that his comments may have been informed by a meeting between his security adviser John Bolton and the ERG, a group of strongly pro-Brexit Conservative Party MPs.
The Queen has met every United States president since Harry Truman - except for Lyndon Johnson, who didn't visit Britain while in office - during her 66-year reign.
Trump attacked British Prime Minister Theresa May's recently released plan for the U.K.'s departure from the European Union, saying the plan-which keeps Britain closely aligned with the E.U. on certain regulatory matters-would "probably kill" the chance of a trade deal with the U.S.
"The people voted to break it up so I would imagine that's what they would do, but maybe they're taking a different route, I don't know if that is what they voted for".
British Prime Minister Theresa May greets USA president Donald Trump at Chequers. The president began his day reviewing a military exercise alongside May at the Royal Military Academy Sandhurst.
Later, Trump will go to Windsor Castle for tea with 92-year-old Queen Elizabeth.
May will host a black-tie dinner for Trump there, attended by senior ministers and about 100 business leaders, including from Blackstone group, Blackrock, Diageo, McLaren and Arup. "She has got a great and lovely grace about her", he added. I think she is a nice person. "Now he might not like the current president, but I represent the United States".
In a statement, Ms Sanders said: "The President likes and respects Prime Minister May very much". It is not considered appropriate to call the Queen by her first name - a gaffe that Nelson Mandela made in 2014 - and it is never okay for people to use her nickname Lilibet, which is reserved exclusively for very close family members.
She'll also be hoping Mr. Trump ignores the thousands of people protesting his visit.
In the Sun interview, which was conducted during Wednesday's North Atlantic Treaty Organisation summit in Brussels, Trump renewed attacks on Mayor of London Sadiq Khan, with whom he has a long-running feud.
Trump went on: "You have a mayor who has done a bad job in London". The president claimed Europe is "losing its culture" because of immigration from the Middle East and Africa. Dozens of demonstrations are planned throughout the country with the largest expected to take place in central London on Friday. "I think they agree with me on immigration". "I think he has done a bad job on crime, if you look, all the terrible things going on there, with all of the crime that is being brought in".
Trump's Marine One departure from the ambassador's residence was met by jeers from demonstrators banging pots and pans, and another pack of protesters lined roads near the palace. Some signs read "Dump Trump", "Lock Him Up" and "There Will Be Hell Toupee". Police worked overtime, their days off canceled. Mr. Trump has been a keen supporter of Brexit and on Thursday he appeared to echo those concerns.
Mr Trump and First Lady Melania landed in Britain on Thursday.
The mood was far less jovial in Belgium earlier in the day.
After a North Atlantic Treaty Organisation summit where he provoked a crisis session to force allies to raise their defense spending, Trump landed in Britain having described the closest USA ally in Europe as being in turmoil over Brexit. But there was little evidence they had bowed to his wishes on that front.
Trump claimed member nations had agreed to boost their defense budgets significantly and reaffirmed - after days of griping that the USA was being taken advantage of by its allies - that the U.S. remains faithful to the accord.
On CNN, Stephen Collinson also said Mr Trump had detonated a "Brexit bomb" and delivered an "astonishing political knifing" to Mrs May.