In an interview, the US president-elect said he would be inviting Theresa May for early talks in Washington following his inauguration on Friday.
In contrast to Barack Obama, who said Britain would be at the “back of the queue” when it came to a trade deal with the US, Mr Trump made clear it would be a priority for his administration.
“We’re gonna to work very hard to get it done quickly and done properly. Good for both sides,” he said.
“I will be -meeting with (Mrs May). She’s requesting a meeting and we’ll have a meeting right after I get into the White House. I think we’re gonna get something done very quickly.”
His comments came as the Prime Minister prepared to set out her strategy for the forthcoming Brexit negotiations in a major speech on Tuesday.
He disclosed that the Prime Minister had written to him shortly after Christmas with a copy of Winston Churchill’s address to the -Americans after the Japanese attack on Pearl Harbour.
In her letter, she said she hoped the feeling of “unity and fraternal association” between the two countries was “as true today as it has ever been”.
Speaking to Michael Gove for The Times, the former cabinet minister and co-leader of the Leave campaign, Mr Trump also made clear that, unlike Mr Obama, he welcomed the result of last June’s referendum vote.
“People, countries want their own identity and the UK wanted its own identity. Brexit is going to end up being a great thing,” he said.
In a wide-ranging interview, Mr Trump disclosed:
- He wants a new arms control agreement with Russia, saying the numbers of nuclear weapons should be “reduced very substantially”.
- Orders will be signed next Monday strengthening America’s borders which could include travel restrictions on Europeans coming to the US as well as “extreme vetting” of those entering from parts of the world known for Islamist terrorism
- He believes chancellor Angela Merkel made a “catastrophic mistake” when she threw open Germany’s borders to hundreds of thousands of migrants.
In his first UK interview since becoming president-elect, Mr Trump identified the refugee crisis as one of the key factors driving the Brexit vote.
“I do believe this, if they (EU countries) hadn’t been forced to take in all of the refugees, so many, with all the -problems that it . . . entails, I think that you wouldn’t have a Brexit,” he said.
“It probably could have worked out but this was the final straw, this was the final straw that broke the camel’s back.”
Despite having prompted fears of a new arms race last year when he said the US needed to “greatly strengthen and expand” its nuclear capability, Mr Trump indicated he would like to strike a new nuclear deal with Russia.
“For one thing, I think nuclear weapons should be way down and reduced very substantially, that’s part of it,” he said.
But while he would like to make “some good deals” with Russia, he said Moscow’s intervention in Syria had been “a very bad thing” which had created a “terrible humanitarian situation”.
Mr Trump was highly critical of US foreign policy, describing the invasion of Iraq as “possibly the worst -decision ever made in the history of our country”, -likening it to “throwing rocks into a -beehive”.
He said Afghanistan was “going badly” while the offensive to retake Mosul - the Islamic State terror group’s last stronghold in Iraq - had turned out to be a disaster.
Mr Trump, however, spoke warmly of how he was looking -forward to visiting Britain, saying his Scottish mother was “so proud of the Queen”.
“Any time the Queen was on television, an event, my mother would be watching,” he said.
He joked that his Scottish -ancestry meant he liked to “watch my -pennies”, adding: “I mean I deal in big -pennies, that’s the problem.”