Donald Trump has pledged to move “very quickly” in securing a trade agreement with Britain after Brexit and predicted that leaving the European Union would be a “great thing” for the UK.

In an interview published in The Times with Michael Gove, the former Justice Secretary and prominent Leave campaigner, the President-elect suggested the fall in the value of the pound was “great” because “business is unbelievable in a lot of parts in the UK”.

“I think Brexit is going to be a great thing,” he added. “I thought the UK was so smart in getting out.”

His comments came as sterling fell 1.5 per cent against the US dollar, to its lowest levels since October amid speculation Theresa May is preparing to announce she is willing to leave the EU’s tariff-free market in a major speech at Lancaster House on Tuesday.

When asked whether he would move quickly on a potential trade deal once Britain has left the EU, Mr Trump, who is set to be inaugurated as the 45th President of the United States on Friday, said: “Absolutley. Very quickly. I’m a big fan of the UK we’re gonna work very hard to get it done quickly and done properly. Good for both sides.”

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Mr Trump, however, dodged a question on whether Britain would be at the “front of the queue” for a trade deal – a reference to Barack Obama’s “back of the queue” intervention during the EU referendum campaign.

In late 2016, two of Ms May’s most senior aides, Nick Timothy and Fiona Hill, travelled to Washington to meet some of the President-elect’s closest aides. When the secret mission by the Prime Minister’s joint chiefs-of-staff was made public earlier this month, a Government source said it was part of the process leading towards the Prime Minister’s first visit in the spring.

Mr Trump told The Times: “ I will be meeting with [Theresa May] – in fact if you want you can see the letter, wherever the letter is, she just sent it. She’s requesting a meeting and we’ll have a meeting right after I get into the White House and... we’re gonna get something done very quickly.”

Sir Kim Darroch, the British ambassador to the US, has previously suggested the so-called special relationship will continue and that the two leaders will “build on the legacy” of Ronald Reagan and Margaret Thatcher.

The interview also comes after a poll by ComRes for The Independent suggested up to half the British public believe the Prime Minister should pursue a close relationship with the incoming President because it is in Britain’s best interest to do so. The poll found that 49 per cent supported a close relationship, while 31 per cent thought it would be better for Downing Street to turn its back on the new American administration. The other 20 per cent said they didn’t know.

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In the hour-long interview with Mr Gove, who rejoined The Times as a columnist last year after he was sacked by Ms May, the President-elect also revealed his mother’s admiration for Queen Elizabeth II. “Any time the Queen was on television, an event, my mother would be watching,” he added.

It makes Mr Gove the second British politician to have met with Mr Trump since his victory over Hillary Clinton in the American elections last year. Nigel Farage, the former Ukip leader, met the billionaire business mogul at Trump Towers in New York shortly after his electoral victory.