The state visit was never actually scheduled - there has been fierce opposition to it in many quarters of Britain - and this trip is part of a working visit instead, meaning among other things that Mr. Trump will overnight at Winfield House, the US ambassador's handsome residence near Regents Park, rather than at Buckingham Palace or Windsor Castle as a guest of the queen.
"The president knows how important the special relationship is firsthand and that's why the bust of Churchill is actually in the Oval Office as we speak".
Mr Trump is coming direct from Brussels, where he was one of the main protagonists of the two-day North Atlantic Treaty Organisation summit.
"I just want the people to be happy".
May's government has recently been shaken following at least three resignations of senior members of her cabinet - including Foreign Secretary Boris Johnson and Brexit Minister David Davis, following disagreements on how to exit the EU.
"So I would imagine that's what they will do, but maybe they will take a little bit of a different route".More news: Clubs line up to sign Manchester United's Victor Lindelof
Speaking about the protests - that includes a giant balloon baby flown over Parliament - Trump told reporters in Brussels that he was well-regarded by Brits.
May is trying to unify her deeply divided Conservative Party behind her Brexit plans with some of her own lawmakers openly speaking of a leadership challenge.
Britain "is in somewhat turmoil", Trump said before departing Washington, remarking that dealing with Putin might surprisingly be the easiest part of the European trip.
In the busy south London neighborhood of Brixton, Victor Greetham, who runs a jazz bar, said he hasn't been to a demonstration since he protested against the Iraq War in 2003, but he planned to attend one of the protests against Trump's visit.
The visit is seen as crucial at setting the course for a closer trading relationship between the two countries.More news: Trump Says Drugmaker Pfizer Should Be "Ashamed" For Drug Price Hikes
He said: 'They like me a lot in the UK.
But Drew, an American student who lives here in the United Kingdom, won't be among the demonstrators.
The prime minister will host a gala dinner and a meeting with Trump, giving them time to talk.
The two leaders are also expected to discuss Russia, Brexit and Middle East.
Mr and Mrs Trump will head to Scotland for the weekend, where they aren't expected to be involved in any official commitments.More news: Harry, Meghan mobbed by fans on first official visit to Ireland