Mr Trump raised eyebrows when he went out of his way to praise Boris Johnson after resigning as foreign secretary, while insisting it was up to the British people whether Mrs May remained in office or not.
More than 50,000 people have signed up to demonstrate in London, where they intend to fly an oversized balloon depicting the president as an angry baby in a diaper.
Labour Party legislator Paul Flynn, who has criticized Mr. Trump in Parliament, says the USA leader has outraged Britons - and people around the world - with his harsh treatment of immigrants.
Months earlier, in February, Trump had gone after the UK's National Health Service, saying it's facing financial woes and accusing Democrats of seeking a similar universal health care system for the United States.
"Give us your tired and your oppressed and we'll divide you from your children", he said mockingly of Mr. Trump's policies.
Due to the thousands of people due to protest against him in London, Trump is largely avoiding the capital other than a quick stop at the U.S. embassy. The lawmakers even had the support of an online petition signed by almost 2 million people wanting May to avoid the US's company over Trump's executive order on immigration.
Trump arrives in Britain on Thursday after the North Atlantic Treaty Organisation summit in Belgium and will stay overnight at the central London residence of the USA ambassador, where a high metal security fence has been erected outside.
Trump is also expected to travel to Scotland, where he owns two golf courses.
Trump postponed his trip several times as a petition to block him from entering the United Kingdom gained so many signatures that it was debated in parliament.
"There is no stronger alliance than that of our special relationship with the US and there will be no alliance more important in the years ahead", the British leader said.
The petition against Trump claimed an official state visit would be embarrassing for the Queen.
Trump will spend Thursday night in London at Winfield House, the official residence of U.S. Ambassador to Britain Robert "Woody" Johnson.
Nearly all of Trump's activities will be outside the city: He'll meet the Queen at Windsor Castle, not Buckingham Palace.
Trump has hit out at Mayor of London Sadiq Khan after the London Bridge terrorist attack, taking Khan's quote of "no reason to be alarmed" out of context and making it seem as if Khan was playing down the significance of the attack.
The President and the First Lady will attend a dinner, hosted by May, at Blenheim Palace - the ancestral home of Winston Churchill - on Thursday evening.
On Friday, he will visit off-camera a British military base and will have a working lunch at Chequers with the Prime Minister, where a number of issue including trade and Brexit will be discussed.
Mrs May will be seeking to improve her often publicly strained relationship with he United States president as she pushes for a post-Brexit trade deal with America. Separately, his wife, Melania, will visit war veterans and schoolchildren in a London visit accompanied by Philip May, the prime minister's husband.
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