US secretary of state Rex Tillerson.
Instead, it had been expected that Trump would make a brief, less formal working visit next month, to cut the ribbon on the $1bn (750m) embassy in Nine Elms, south-west London, and hold meetings with May.
Officials had been examining plans for the president to meet the Queen, without the pomp of a full-blown state banquet, with the attendant risk of disruptive protests.
However, even that more modest plan now appears to have been abandoned for the time being. Government sources suggested that Washington had signalled that secretary of state
Rex Tillerson would instead open the multimillion-pound embassy.
Trump confirmed on Twitter late on Thursday night that the trip was off. Reason I canceled my trip to London is that 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 just before midnight local time. Bad deal. Wanted me to cut ribbon-NO!
Citing security and environmental reasons, the US state department agreed to sell the current embassy building in Grosvenor Square to the Qatari Diar Real Estate Investment Co, which intends to turn it into a luxury hotel.
Estimates put the sites value at 500m before it was made a listed building, which would have diminished the value because of restrictions on development.
Relations with the controversial president hit a low late last year when May criticised his decision to retweet material posted by the far right extremist group, Britain First.
Trump responded by tweeting directly to the prime minister that she should focus on tackling domestic terrorism.
The government was so concerned about his decision to share the extremist videos that Britains ambassador to Washington, Sir Kim Darroch, took the rare step of raising the issue directly with the White House.
Trumps ambassador to London, Woody Johnson, subsequently insisted: The president and the prime minister have a very, very good relationship. I know the president admires and respects the prime minister greatly.
He added: My job and the presidents job is to protect Americans. Hes doing the best that he can.
Youre going to have little stumbles along the road. Absolutely. Youre going to have things that happen. But the intent is there and its genuine, and its going to happen.
Mays government has been keen to strike up a close working relationship with the Trump administration despite his erratic behaviour, because of Britains desire to strike a swift trade deal with the worlds largest economy.
When the PM visited the White House, she was pictured holding hands with the president.
Trump has sparked alarm among diplomats by repeatedly entering into Twitter spats with key public figures, including North Korean leader Kim Jong-un, to whom he recently boasted about the size of the US nuclear arsenal.
Donald Trump and Theresa May hold hands as they walk along the colonnade of the White House in Washington. Photograph: Olivier Douliery/EPA
The White House has been rocked in recent days by the revelations in an explosive book, Fire and Fury, by the US journalist Michael Wolff, who suggested even senior figures in the administration questioned the presidents fitness for office.
Asked about the revelations last weekend, May said she believed they were not serious, and Trump was a man making decisions, in the interests of the United States.
Trump faced fresh criticism on Thursday night after the Washington Post reported that he had questioned planned changes to immigration rules,
asking colleagues why the US had to welcome arrivals from shithole countries.
The president is expected to be the biggest draw at the World Economic Forum in Davos later this month, where politicians and business leaders gather each year to network, and discuss the pressing issues facing the international economy.
After Trumps inauguration last year, thousands of people joined a
Womens March in London, echoing similar protests in Washington and other capitals, against his misogynist comments and behaviour.
Downing Street refused to confirm that the visit had been cancelled on Thursday night, with a spokesman repeating the governments longstanding position that an invitation has been extended and accepted, but no date has been set.
Asked about the reports, White House press secretary Sarah Sanders emailed a response that said: The invitation was made and has been accepted we are still working to finalise a date.