In an interview with Britain's Sun newspaper published late on Thursday, Trump said May's plans for a business-friendly Brexit would leave it too close to the European Union to allow a new trans-Atlantic trade deal to be struck.
A high metal fence has been erected around the US ambassador's central London residence where Trump will spend Thursday night and the embassy has sent out an alert warning Americans in London to keep a low profile in case protests turn violent.
Trump is expected to arrive after a North Atlantic Treaty Organisation summit in Belgium and will meet with Prime Minister Theresa May, meet Queen Elizabeth at Windsor Castle, and will attend a black-tie dinner at the home of former World War Two leader Winston Churchill.
Trump also said that Boris Johnson, who had resigned as foreign secretary on Monday in protest of May's recent announcement of a plan for Brexit, was "a very talented guy" who "would be a great prime minister".
Trump's remarks, made in a bombshell interview with The Sun published Thursday during his first visit to Britain as U.S. president, are an explosive intervention into British politics that seem likely to cause political chaos and imperil the prime minister as she attempts to negotiate Britain's exit from the European Union. Asked how he felt about the tens of thousands of protesters awaiting him in Britain, he insisted: "I think they like me a lot in the UK".
A balloon depicting a baby Trump was allowed to fly over London by mayor Sadiq Khan.
Mr Trump said he had told Ms May how to do a Brexit deal, but the Prime Minister did not heed his advice. I think she is a nice person.
Mr Trump and his wife Melania arrived at Stansted airport, where he was met by the UK's global trade secretary Liam Fox.
New US Embassy in London
Mr Trump had already cast doubt on Ms May's Brexit plans earlier in the day after a North Atlantic Treaty Organisation summit in Brussels, where he provoked a crisis session to force allies to raise their defence spending.
He will hold talks on foreign policy with Mrs May at Chequers, before meeting the Queen at Windsor Castle - 26 miles from the capital.
But the Environment Secretary said he was not sure he possessed the "diplomatic skills" to bring Mr Trump round to his line of thinking.
Speaking about the prime minister's strategy, President Trump said, "I would have done it much differently".
Protests took place outside the Blenheim grounds in Woodstock, Oxfordshire, with several hundred demonstrators waving banners and placards reading Dump Trump, Not Welcome Here, Protect Children Not Trump and Keep Your Tiny Hands Off My Pussy!
The interview posted online as Prime Minister May welcomed President Trump and the first lady at Blenheim Palace for a lavish gala dinner. Trump is technically on a lower-level working visit this week. "Now he might not like the current President, but I represent the United States", he said. Trump's late mother hailed from Scotland, and he owns two luxury golf courses there.