Theresa May invited Trump for a state visit when she became the first world leader to visit the president in the White House a year ago.
With activists pledging to stage mass protests and MPs determined not to give the president the opportunity to address parliament, no date for a state visit has been set.
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.
Trump confirmed on Twitter that the trip was off.
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 Britain’s ambassador to Washington, Sir Kim Darroch, took the rare step of raising the issue directly with the White House.
Trump’s 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 president’s job is to protect Americans. He’s doing the best that he can.
“You’re going to have little stumbles along the road. Absolutely. You’re going to have things that happen. But the intent is there and it’s genuine, and it’s going to happen.”
May’s government has been keen to strike up a close working relationship with the Trump administration despite his erratic behaviour, because of Britain’s desire to strike a swift trade deal with the world’s 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.
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 president’s 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 Trump’s inauguration last year, thousands of people joined a Women’s 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 government’s 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.”
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