The president described Britain as a "hot spot" with "a lot of resignations", and added that his trip next week to Helsinki to meet President Putin may be comparatively easier.
But while Trump's Friday morning plans involve a visit to a military site with May, followed by their joint press conference at Chequers, the first lady is expected to remain in London, in the company of May's husband, Philip May.
Despite not being an official state visit, the Government is desperate to ensure the USA leader feels he is being treated with the appropriate level of pomp and ceremony.
Trump was flying over after a fraught North Atlantic Treaty Organisation summit in Brussels where he piled pressure on allies to double their defence spending.
"So I would imagine that's what they will do, but maybe they will take a little bit of a different route".
May hopes Trump, who landed at Stansted airport before flying by helicopter to the U.S. ambassador's London residence, will help to accelerate a future free trade deal, though his public comments on Brexit cast a shadow over the visit.
The controversial 45th President of the United States will visit the UK for the first time in his position on Thursday, July 12. "They want the same thing I want", he said.
The people who started the campaign say that the balloon is a means to ensure that Trump "knows that all of Britain is looking down on him and laughing at him".
Trump's itinerary will keep him out of central London on Friday, when large protests are planned.
May said in remarks during a banquet on Thursday with Mr. Trump at Blenheim Palace, Churchill's birthplace.
Another man, who did not wish to give his name, said: "It was very complimentary to England and to the allies that we have, very positive".
Some British citizens are even more distressed about Trump than they are about the U.K.'s own feverish political turmoil. "I like Boris Johnson, I've always liked him", said Mr Trump.
Many Britons are opposed to Trump's trip which is not the full state visit he was originally promised with the pomp and ceremony that entails.
Mr. Trump may have ruffled feathers again when he said just before departing for Europe that the United Kingdom was in "turmoil", suggesting it was "up to the people" to decide if Prime Minister Theresa May remains in power after a few days that saw her authority challenged by the resignation of two prominent Cabinet ministers protesting her Brexit policy.
"This week we have an opportunity to deepen this unique trading relationship and begin discussions about how we will forge a strengthened, ambitious and future-proof trade partnership".
"There is definitely a sense that Britain needs America more because of Brexit", said Bronwen Maddox, head of the Institute for Government, a think tank.
"I think they like me in the UK".
Italian Prime Minister Giuseppe Conte told reporters his country has no plans to increase defense funding.
On Friday, Trump will meet with the prime minister and the Queen and then spend the weekend at one of his private golf courses in Scotland.
Mr Trump's son Eric has arrived in Scotland for a golfing visit to Trump International Golf Links at Menie, Aberdeenshire, and Trump Turnberry, near Girvan, South Ayrshire.
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