Mr Trump’s sudden decision to cancel the visit left Downing Street on the back foot, and the White House is not believed to have provided any more context than his supposedly disapproval of the US embassy’s relocation.
In a tweet last week, Trump blamed his predecessor, former president Barack Obama, for the decision to sell the existing embassy, which he describes as “the best located and finest” in the city, for “‘peanuts.'”
He said: ”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. Bad deal. Wanted me to cut ribbon-NO!”
However, the decision to move the embassy from Grosvenor Square to Nine Elms was made in 2008 under George W. Bush.
It has been suggested President Trump took umbrage with a rebuke from Mrs May after he appeared to endorse a far-right British group, Britain First, on Twitter by retweeting some of their leader’s anti-Muslim messages.
Mrs May’s attendance in Davos is yet to be officially confirmed by Number 10, but this year’s gathering looks set to be one of the most high profile in recent years.
German Chancellor Angela Merkel and French President Macron are expected to be among the 60 world leaders attending.
While she has stopped short of criticising Trump directly, Ms Merkel has vocally disapproved of his policies.
Last year she said: “Globalisation is seen by the American administration more as a process that is not about a win-win situation but about winners and losers.”
The cancellation of Mr Trump’s trip to London saves the Metropolitan Police a huge headache as it was believed there would be large protests in the capital.
Americans living in Switzerland have been warned by the US embassy to expect protests against President Trump.