President Donald Trump said on Friday he had a very strong relationship with British Prime Minister Theresa May, having earlier scorned her Brexit strategy, which he said had probably killed off hope for a future US-British trade deal.

In an interview published just hours before he was due to have lunch with May and tea with Queen Elizabeth on Friday, Trump chided the "very unfortunate" results of the prime minister's strategy for negotiating Britain's departure from the European Union.

"If they do a deal like that, we would be dealing with the European Union instead of dealing with the UK, so it will probably kill the deal," Trump told the Rupert Murdoch-owned Sun newspaper.

"I would have done it much differently," he told The Sun, which urged its readers to back Brexit before a referendum in June 2016. "I actually told Theresa May how to do it, but she didn't listen to me."

Trump also heaped praise on Boris Johnson, who resigned as foreign secretary this week along with Brexit Secretary David Davis in protest at May's strategy. Johnson, the president said, "would be a great prime minister".

No sitting US president has ever made such biting public criticism of a British prime minister while visiting, and his comments undermined May in her party, her country and abroad.

But, as the leaders met for talks at May's official country residence Chequers, both tried to play down the president's intervention, made a few hours after the formal publication of May's plan, in the Brexit debate.

"We really have a very good relationship," Trump said. "Today we are talking trade and we are talking military."

Asked by a U.S. reporter if he regretted his comments to the Sun, Trump looked away and shook his head.

"We've got a lot to discuss," May said, adding they would talk about the British-US "special relationship" and opportunities for a trade deal.

POUND DROPS

Sterling fell half a percent to a 1 1/2-week low of $1.3131, partly on Trump's comments in the newspaper interview.

"Where are your manners, Mr President?" asked Sam Gyimah, a junior minister in May's government.

As Britain prepares to leave the EU on March 29, 2019, supporters of Brexit have made much of the so-called special relationship with the United States and the benefits of forging closer trade ties with the world's biggest economy.

Many have cast May's plan as a betrayal, including lawmakers in her deeply divided Conservative Party, who have warned that she might face a leadership challenge.

On a visit to London two months before the 2016 Brexit referendum, former U.S. President Barack Obama said Britain would be at the "back of the queue" for a trade deal if it departed the EU, an intervention condemned by those backing the 'Leave' campaign such as Johnson.

However, Jacob Rees-Mogg - a leading Conservative Brexiteer and considered a potential alternative party leader by some - said it was perfectly reasonable for Trump to make such comments, adding that May now had an opportunity to change her mind on her Brexit plan.

Still, Trump's comments upset even some who were in favour of the visit. "What he has done, and in particular for me the condescending nature of his comments towards the prime minister ... are unacceptable, undiplomatic and counterproductive," Simon Fraser, a former top official at the UK Foreign Office, told Sky News.

Demonstrators protest against the visit of US President Donald Trump, in central London.Demonstrators protest against the visit of US President Donald Trump, in central London.

TRUMP PROTESTS

For supporters, Trump and Brexit offer the prospect of breaking free from what they see as obsolete institutions and rules. But for many British diplomats, Brexit marks the collapse of a 70-year strategy of trying to balance European integration with a U.S. alliance based on blood, trade and intelligence sharing.

Trump has frequently angered British politicians. Late last year, May criticised him for retweeting a message by a member of a British far-right group, and the speaker of parliament has said Trump would not be welcome to address the chamber.

Thousands of protesters massed in central London for a noisy demonstration against Trump, one of the more than 100 rallies expected during his four-day visit. Protesters flew a blimp depicting the U.S. president as an orange, snarling baby outside the British parliament.

"It's embarrassing how much our government is falling over themselves to try to appease someone who has no interest in any sort of give-and-take in the UK-U.S. relationship at all," said protester Nicola Tanner, 33, from Bristol, southwest England.

On Thursday, May invoked World War Two leader Winston Churchill as she addressed Trump and business leaders at a lavish dinner in his honour at Blenheim Palace, the 18th century country house where Churchill was born.

"Mr. President, Sir Winston Churchill once said that 'to have the United States at our side was, to me, the greatest joy'," May told Trump, according to a text of her speech. She said the United States was "not just the closest of allies but the dearest of friends".

While Trump's trip was not a full state visit, he has been given red carpet treatment including marching military bands. He is scheduled to have tea with Queen Elizabeth at Windsor Castle where her grandson Prince Harry married U.S. actress Meghan Markle in May.

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