The American president claimed on Twitter that his reason for calling off the trip was his displeasure at Barack Obama having sold the current embassy for "peanuts" and built a replacement for $1.2bn. The move was announced in October 2008, when George W. Bush was president.
On the embassy web page about the project, it said: "The project has been funded entirely by the proceeds of the sale of other US Government properties in London, not through appropriated funds".
While the trip was always meant to be a working one, and separate to an official full state visit this year for which a date has not been set, as president Trump has visited more than a dozen countries ahead of Britain, including Belgium, China, France, Germany, Israel, Italy, Japan, the Philippines, Poland, Saudi Arabia, South Korea and Vietnam.
Due to open in mid-January, Trump's visit had been expected at the end of February.
The "strong and deep" partnership between Britain and the United States "will endure" despite Trump's cancellation, a spokesman was quoted as saying by the BBC.More news: Most Inspiring, Confusing and Bizarre Moments at the Critics' Choice Awards
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Madame Tussauds said it made a decision to take their wax Trump figure out on a field trip after the real-life president announced he was cancelling his trip. Lammy tweeted. "You finally got the message that you'd be met by millions of us out on the streets protesting". Trump blamed the Obama administration for the move, accusing it of selling the old embassy for "peanuts" in a "bad deal".
Downing Street later said the "strong and deep" partnership between Britain and the USA "will endure".
Trump was embroiled in a public spat with British Prime Minister Theresa May late past year after he retweeted three anti-Muslim videos from far-right group Britain First.
"He's been to countries all over the world and yet he's not been to the one with whom he's closest", Farage told BBC Radio Four's Today programme.