Three months ago Boris Johnson, then a relatively new Foreign Secretary, instructed his officials to do more to forge links with Mr Trump’s campaign, fearing that there was too much expectation in the Foreign Office of a victory for Hilary Clinton.

Bill and Hilary Clinton
 US Democratic presidential candidate Hillary Clinton makes a concession speech after being defeated by Republican President-elect Donald Trump, as former President Bill Clinton looks on in New York. Credit: AFP/AFP

It has also been claimed that Sir Kim Darroch, Britain’s ambassador to the US, did not do enough to develop close links with Mr Trump’s campaign in the build-up to the presidential election.

On Thursday Philip Hammond said the delay in talks between Mr Trump and Mrs May was because the pair had no “urgent business”.

“We do not have any urgent business that we need to transact,” the Chancellor said. “Obviously, in due course the Prime Minister will be looking forward to meeting Mr Trump once he is inaugurated as the President.

“I expect that the very strong and close relationship that always develops between a UK prime minister and US president will develop between those two.”

But Mr Farage says that he is the only British politician who has “offered help or support” to Mr Trump.

Mr Farage says that he perceived snubs towards Mr Trump have damaged the relationship between the UK and USA.

He says: “Of Britain’s relationship there is going to be a slightly difficult start. Nobody in the British government has reached out to his campaign, believing as with our referendum that he could not possibly win.

“The traditional relationship between the British Conservative party and the Republicans has completely broken down.”

Any issue between Mr Trump and Mrs May goes back to December 2015, when Mr Trump was criticised by the then Home Secretary over his suggestion that he wanted to ban all Muslims from America.

President Barack Obama and Theresa May
U.S. President Barack Obama (R) greets British Prime Minister Theresa May as he arrives for a luncheon during the United Nations General Assembly at United Nations headquarters in New York in September.  Credit: Reuters/Reuters

Mrs May said that the comments were “divisive, unhelpful and wrong”.

Mr Johnson, who was mayor of London at the time, said his views were “ill-informed” and “complete and utter nonsense”.

Mr Trump was also left furious after MPs in Parliament debated whether Mr Trump should be banned from the UK, even threatening to withdraw £600 million of planned investment in Scotland.

Before speaking to Mrs May at 1.45pm on Thursday, Mr Trump spoke to the leaders of Egypt, Ireland, Mexico, Israel, Turkey, India, Japan, Australia and South Korea.

It is traditional for one of a President-elect’s first calls to be to the British prime minister in recognition of the long-standing “special relationship”.

“What is really important now is to accept that he is president-elect, that he will be president, and that whatever the things were said and judgements  made during the campaign, we now have to deal with who will be in the Oval office.”Sir Christopher Meyer

Sources close to Mr Trump insisted that the order of the calls was random. They said that proper plans had not been put in place for the day after the election.

Following the call Downing Street said: “The Prime Minister and President-elect Trump agreed that the US-UK relationship was very important and very special, and that building on this would be a priority for them both.

“President-elect Trump set out his close and personal connections with, and warmth for, the UK. He said he was confident that the special relationship would go from strength to strength.”

Government sources confirmed that Dr Fox will travel to America “as soon as possible” to attempt to “engage” with Mr Trump’s team.

Mr Trump invited Mrs May to the White House during their phone call on Thursday. It is expected that the Prime Minister will fly to Washington early next year.

Sir Christopher Meyer, who was Britain’s ambassador in Washington from 1997 and 2003, said it had been difficult for British officials to know who to speak to around Mr Trump.

He said the UK had to speak “either to the family” or to other figures like Governor Chris Christie or Newt Gingrich but it was not clear to what extent they are “authentic spokespeople for Donald J himself”.

He added: “It must be more difficult to get alongside Donald than it was for me to get alongside George W [Bush] or my predecessor to get alongside Bill Clinton.”

He said: “What is really important now is to accept that he is president-elect, that he will be president, and that whatever the things were said and judgements  made during the campaign, we now have to deal with who will be in the Oval office.

“And that means cracking on with messages of congratulation, the embassy going ‘full roar’ to get alongside those who are going to be in the new administration.”