May hosts Trump on Thursday for a black-tie dinner with business leaders at Blenheim Palace, the birthplace of Second World War prime minister Winston Churchill, and on Friday, the pair will visit a defence site before travelling to the prime minister's Chequers country residence for talks followed by a press conference.
On Friday, Trump's official events were all set for outside London, away from the major protests, which appeared to be a concession to his famously thin skin.
His highly controversial remarks came at the end of a day in which he had already waded deeply into the Brexit row over May's Brexit vision. It would see Britain follow European Union rules on goods to protect cross-border trade and avoid checks on the Irish frontier, while enabling it to control migration and sign new non-EU trade deals, including in services.
But Mr Trump appeared to link Brexit to the current trade dispute between the U.S. and European Union over steel and aluminium. That announcement sparked several high-level resignations-including Foreign Secretary Boris Johnson and Brexit Secretary David Davis.
Trump is meeting May for a working lunch before meeting the Queen for tea and a likely round at his Scottish golf course. This is what White House spokespeople do when a statement they're tasked to deliver is ridiculous and they'd rather attribute it to Trump rather than sacrifice their own credibility.
But he praised Mrs May as a "very tough negotiator" and described her as an "incredible woman" who is "doing a fantastic job". It's a much different deal than people voted on.
Donald Trump has used his first press interview during his visit to the United Kingdom to lay into Theresa May's plans for Brexit and hail Boris Johnson as a future prime minister, as well as continuing his war of words with London mayor Sadiq Khan. I am just saying I think he would be a great Prime Minister.
According to The Sun, Trump said May not only ignored the advice he gave her on Brexit, but has gone "the opposite way", leading to "very unfortunate results".
Some 51% of Britons think Mr Trump was right to make his views on Brexit public, while 45% think he should have kept them private - 4% did not know.
Think your friends would be interested? "I have a lot of respect for the prime minister. I think it's a very negative thing for Europe".
When asked what he hopes to accomplish in his meeting with Russian President Vladimir Putin on Monday, Trump said they would be talking about Ukraine, Syria and other parts of the Middle East as well as nuclear proliferation.
However, the president also suggested that the dispute with Khan was personal and that the mayor had shown disrespect to him by allowing a 20-foot "Trump Baby" balloon - an orange likeness of Trump wearing a diaper - to fly over London protests during the president's visit. The President told the newspaper he was aware of the blimp, saying, "I guess when they put out blimps to make me feel unwelcome, no reason for me to go to London".
"I look at cities in Europe, and I can be specific if you'd like".