Trump "has proudly sparked passionate often divisive emotions about things, I think Americans living here to eager to turn out and express their views", he said.
A giant six-metre-high blimp of Trump depicted as an orange baby in nappies is also expected to fly over the capital.
Queen Elizabeth II has outlasted 13 USA presidents during her reign.
They are expected to be in Scotland until Sunday.
Asked about Trump's comments, May said: "We're delivering on the vote of the British people to take back control of our money, our laws and our borders". "But maybe they're taking a little bit of a different route, so I don't know if that's what they voted for".
Fielding questions following the North Atlantic Treaty Organisation summit in Brussels, Mr Trump was asked his views on Britain's withdrawal from the European Union, suggesting it may deliver a softer Brexit that was not what the public wanted.
But the president will avoid London nearly entirely during his trip, which has been characterised as an attempt to avoid humiliation over the planned protests surrounding his visit.
"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.
Trump has always been a Brexit supporter and has expressed enthusiasm for a wide-ranging trade deal with Britain after Brexit, something heralded by eurosceptics as being one of the great benefits of exiting the bloc.
Opponents to the controversial U.S. leader have threatened mass protests but Mr Trump is expected to avoid areas such as central London where demonstrators are likely to gather.
"I would be happy to see Hillary Clinton if she was president visit the UK".
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 USA ambassador's handsome residence near Regents Park, rather than at Buckingham Palace or Windsor Castle as a guest of the queen.
Later in the day, Mr Trump will travel to Blenheim Palace, the 18th-century stately home where Britain's World War II leader Winston Churchill was born and spent most of his childhood.
On Friday, demonstrators are expected to gather near Chequers, the Prime Minister's country residence, where May and Trump will hold a working lunch.
Similar protests are planned on Thursday evening outside the United States ambassador's home at Regent's Park and in Scotland when Mr Trump visits on Saturday.
Mr Trump will spend the weekend in Scotland where he has two golf courses and plans to play at least once.