(AFP) -- Trump said he was abandoning next month's trip because he did not like the location and cost of the new embassy building.
But Foreign Secretary Boris Johnson suggested the decision was prompted by the opposition to Trump in Britain, and warned such critics "seem determined to put this crucial relationship at risk".
Prime Minister Theresa May offered Trump a state visit to Britain one year ago, when she became the first foreign leader to visit the White House after his inauguration.
But the date has yet to be set in the face of deep hostility to the president in Britain, prompting speculation it could be turned into a lower profile trip focused around the opening of the new embassy.
Trump tweeted overnight that he would not attend the ceremony, initially scheduled for next month.
"I am not a big fan of the Obama administration having sold perhaps the best located and finest embassy in London for 'peanuts', only to build a new one in an off location for 1.2 billion dollars," he wrote.
"Bad deal. Wanted me to cut ribbon - NO!"
The embassy move is in fact the result of a decade-long project initiated by the administration of former Republican president George W. Bush.
His decision not to come was welcomed by critics outraged by the US travel ban on Muslim-majority countries, and more recently, Trump's decision to re-tweet anti-Muslim videos posted by a British far-right organisation.
"Many Londoners have made it clear that Donald Trump is not welcome here while he is pursuing such a divisive agenda. It seems he's finally got that message," tweeted Mayor of London Sadiq Khan.
The mayor, a member of the main opposition Labour party, said there would have been "mass peaceful protests", and that it had been a "mistake" to invite him.
There is likely some relief in the British government at Trump's decision, which would have caused at the very least a major policing operation.
But Johnson accused Khan and Labour leader Jeremy Corbyn of damaging US-UK relations with their vocal criticism.
"The US is the biggest single investor in the UK -- yet Khan & Corbyn seem determined to put this crucial relationship at risk," he tweeted.
"We will not allow US-UK relations to be endangered by some puffed up pompous popinjay in City Hall."
A spokesman for May's Downing Street office said the invitation for the state visit "has been extended and accepted. No date has been confirmed".
"The US is one of our oldest and most valued allies and our strong and deep partnership will endure," he said.
Relations between May and Trump became strained in November after he re-tweeted anti-Muslim videos posted by a British far-right group.
May condemned it, and Trump hit back that she should focus on terrorism in Britain, which suffered five attacks last year.
In an article in London's Evening Standard newspaper on Friday, US ambassador Woody Johnson said Washington was "re-investing in the special relationship".
"Our new embassy reflects not just America's special history with the UK but the special future ahead of us as we advance the prosperity and security of both our nations," he wrote.
He conceded that the former building in upmarket Mayfair, central London, was a "perfect location" but noted it was viewed as too vulnerable following the September 11, 2001, attacks.
The new 12-storey, cube-shaped building, designed by American architects KieranTimberlake, is located in a regenerated area on the south bank of the River Thames. It will be open for business on January 16.
A US Embassy spokesperson rejected Trump's criticism of the new building on Friday, calling it "one of the most secure, hi-tech, and environmentally-friendly embassies the United States has ever built", adding that the Nine Elms site "was the best overall location.".
Leading Brexit campaigner Nigel Farage, who visited Trump following his election, said it was "disappointing" the president could not visit when he had been to so many other countries.
But Stephen Doughty, an opposition Labour lawmaker, tweeted: "We are not a big fan of his racist, sexist, unthinking behaviour."
In Trump's absence, the Madame Tussauds museum installed the president's waxwork outside the new embassy, causing construction workers to crowd round and pose for selfies.
(Photo: Protesters holding placards take part in a rally in Parliament Square in February 2017 against US president Donald Trump's state visit to the UK Getty Images)