The president and his wife will attend a dinner, hosted by Mrs May, at Blenheim Palace - the ancestral home of former Prime Minister Sir Winston Churchill - in the evening.
Mr Trump has already caused additional controversy, by again commenting on the vexed debate about how Brexit should be implemented.
The trip coincides with a tumultuous week for May after two senior ministers resigned in protest at her plans for trade with the European Union after Britain leaves next March.
"The people voted to break it up but maybe they're taking a little bit of a different route, so I don't know if that's what they voted for", he said. "I think North Atlantic Treaty Organisation is much stronger now than it was two days ago".
The US President described Britain as a "pretty hot spot right now with a lot of resignations" and suggested his meeting with Vladimir Putin in Helsinki on Monday could be easier.
Ms. May quickly moved to fix the damage. The protocol is that if embassy staff are warned internally about possible threats, then the American public must be as well, she said.
Just hours after May's foreign minister, Boris Johnson, resigned and complained that the Brexit dream was being suffocated, Trump said he might speak to him during the trip.
"The president of the United States of America will regretfully have the red carpet rolled out for him by this Conservative government", Ian Blackford, the Scottish National Party's leader in the Westminster parliament, had told lawmakers on Wednesday.
The poll conducted this week said 63 percent found Trump racist, and 74 percent said he was sexist.
The biggest protest will take place in central London on Friday when thousands are expected to take to the streets to join the "Stop Trump" march.
London Mayor Sadiq Khan - who has had a particularly contentious relationship with President Trump - approved protesters' use of a "Trump baby" blimp during the president's visit to Great Britain.
Anti-Trump demonstrations were expected to take place in Bristol, Newcastle, Leeds, Cambridge and Cardiff.
"Melania has seen photos of the Trump baby blimp, and she doesn't find it amusing in the slightest, she thinks it's mortifying", a source close to the first lady tells HollywoodLife EXCLUSIVELY.
For protesters in Edinburgh they have a particularly varied day to look forward to.
"Inevitably there are a number of factors", he continues, "not only around the profile of someone with the status of Trump coming in, but also the fact that there are many other extraneous measures that need to be considered". Brexit Secretary Dominic Raab told the House of Commons that the plan represented a "principled, pragmatic and ambitious future partnership between the United Kingdom and the European Union".
The economic and trade relationship with the U.S.is also vital: The U.S.is the U.K.'s single largest trading partner. The plan also doesn't deal with trade in services, including financial products, which accounts for 80 per cent of the country's economy.
The British are usually polite to a fault - though they have been known to go off after a soccer match or once the pubs close.
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