The visit comes at a testing time: May is battling to make a success of Brexit and keep her minority government together, while Trump is challenging Western assumptions about free trade and turning away from global institutions.
The couple will then stay at Winfield House, the U.S. ambassador's residence on the edge of Regent's Park in London.
London Mayor Sadiq Khan, a Muslim who has been involved in social media exchanges with the USA president, said Trump was not welcome in the British capital because of his divisive agenda and would face mass peaceful protests.
Trump will arrive from the North Atlantic Treaty Organisation summit in Brussels on Thursday and will attend a black-tie dinner at Blenheim Palace, a country house near Oxford where Churchill was born in 1874. Trump's comments on militant attacks in Britain have sparked anger and he has often exchanged barbs on social media with London mayor Sadiq Khan.
In the evening, May will host a black-tie dinner for Trump at the stately home that will be attended by about 100 business leaders from industries including finance, pharmaceuticals, defence and technology.
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The couple will then stay at Winfield House, the USA ambassador's residence on the edge of Regent's Park in London. And no president in living memory has stoked quite so much controversy around his visit as incumbent Donald J. Trump, a populist strongman who has turned traditional leadership on its head with his brash, unapologetic style that runs contrary to a more conservative and muted British sensibility concerning politics and politeness.
Afterwards, the president will travel to Scotland, where he owns two golf courses.
Asked whether the President's schedule was created to keep him away from possible protests, a Downing Street spokeswoman said: "Prime ministers frequently make use of Chequers for meetings with foreign leaders".
Trump will meet the queen at Windsor Castle on Friday before traveling to Scotland for the rest of that weekend.
A simple "no thank you" has already arrived from a few guests, including Martha Lane Fox, co-founder of Lastminute.com, who told the Financial Times: "I understand why the government have to entertain Trump, but I certainly don't want to". "What does this man have to do to have the invitation that the prime minister has extended revoked?" Blenheim is famed as the birthplace of Winston Churchill.
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The event will begin with a military ceremony featuring the bands of the Scots, Irish and Welsh Guards in the spectacular Great Court.
Hosted by the Prime Minister, guests at the dinner will include leaders of United Kingdom business sectors including financial services, travel, creative industries, food and drink, engineering, tech, infrastructure, pharmaceuticals and defence.
During dinner, an orchestra will perform a series of classic British and American hits and the Royal Regiment of Scotland will pipe the President out at the end.
He said the highlight will be the chance for the president and first lady to meet the queen.
The six-meter-high orange balloon, in the form of Trump wearing a nappy, will fly above Westminster for about two hours on the morning of July 13 to coincide with a "Stop Trump" demonstration in central London which about 50,000 people are expected to attend. This will include a working lunch.
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When Donald Trump meets Queen Elizabeth next week, he will become the 12th United States president that the monarch has met during her 66 years on the throne, the longest in British history.