Mr Trump and his wife Melania flew from London by Marine One helicopter and swept into the palace courtyard in the armoured presidential limousine nicknamed The Beast.
President Donald Trump's visit to Britain includes a gala dinner, tea with the queen and lunch with the prime minster, but his itinerary will keep him out of central London on Friday, when large protests are planned.
He warned she may have killed off any chance of a trade deal with the US.
Brexit "creates an opportunity to reach a free trade agreement that creates jobs and growth here in the UK and right across the United States", she said.
Labour's shadow foreign secretary Emily Thornberry told Sky News she felt sorry for Mrs May, adding: "Donald Trump ought to have listened to his mother".
He said "the deal she is striking is a much different deal than the one the people voted on". "I think he is a great representative for your country".
While the White House had previously denied the president's schedule in London was meant to keep him away from the protests, Trump admitted as much in an interview with the British-owned tabloid "The Sun". The president began his day reviewing a military exercise alongside May at the Royal Military Academy Sandhurst.
Trump is set to join May later on Friday at a display of joint US-UK military might at an undisclosed location before both leaders head to Chequers, the British prime minister's country retreat in Buckinghamshire, for in-depth bilateral discussions.
He went on to say: "There might be protests, but I believe that the people in the UK, Scotland, Ireland, I think those people, they like me a lot". He added, however, that he thought the PM was a "very good person".
"I think it's a travesty of British values".
Referring to the plan outlined on Thursday in which Britain would aim to keep strong ties in trading of goods with the European Union, he said: "The deal she is striking is a much different deal than the one the people voted on".
The Sun said its interview with Trump was conducted in Brussels before he left for the British leg of his trip.
The Trumps arrived at Stansted Airport near London on Air Force One earlier that afternoon for the controversial trip to Britain.
The visual cornerstone of the anti-Trump protests on Friday - which include several organized marches by varying groups - is a giant balloon depicting the US leader as an angry, screaming orange baby in a diaper, clutching a cell phone with Twitter on the screen.
The balloon was authorised by Khan, who has crossed swords with Trump several times after the president posted factually incorrect messages over a series of terror attacks in Britain in 2017.
The agenda for Trump and May on Friday includes discussion on relations with Russian Federation, ahead of a summit in Finland on Monday between Trump and President Vladimir Putin.
"Allowing the immigration to take place in Europe is a sham", he said. You have a mayor who has done a bad job in London. Some of their signs read "Dump Trump", "Lock Him Up" and "There Will Be Hell Toupee".
The US president' four-day visit is expected to cost the taxpayers with a police and security bill of up over US$10 million, the Telegraph has reported.
Trump was greeted at the palace by May, whose government has been rocked by resignations from ongoing tumult over Brexit. But there was something about the flowing buttercup yellow chiffon gown that looked familiar to some, drawing comparisons with Belle from Beauty and the Beast among some other fictional characters.
Fresh from a contentious meeting with North Atlantic Treaty Organisation leaders in Brussels in which he demanded member nations contribute more for their collective defense, Trump made a number of incendiary remarks to the British tabloid that are sure to provide fodder for his critics in the United Kingdom and Europe.
Then, in a head-snapping pivot at the end, he declared the alliance a "fine-tuned machine" that had acceded to his demands to speed up increases in military spending to relieve pressure on the U.S. budget.
She listed Mr Trump's immigration policies, bans on some people entering the U.S., his foreign policies, and lack of support for taking action on climate change as having affects across the globe.
During his news conference on Thursday, the USA president also appeared to refer to Ireland as part of the United Kingdom.