US President Donald Trump today played down his extraordinary attack on Britain's plans for Brexit, praising Prime Minister Theresa May's leadership and insisting ties between the two countries "have never been stronger".

Trump's first official visit to Britain was overshadowed by his scathing criticism of May's plans for leaving the European Union, which risks encouraging a revolt among eurosceptics in her party.

"Whatever you do is okay with us, just make sure we can trade together, that's all that matters," Trump told May after talks at her country retreat of Chequers, as a colourful protest of tens of thousands including a "Trump Baby" inflatable marched through the streets of London.

At a press conference in the grounds of the 16th-century manor house, he repeatedly praised May's leadership, saying she was a "terrific woman" and admitting that Brexit was a "tough situation".

They met just hours after an interview with The Sun tabloid was published, in which Trump said May's plans for close future ties with the EU would "probably kill" her hopes for a US trade deal.

He suggested this was not what voters wanted, saying he had advised May to take another path. He added that Boris Johnson, who quit as foreign minister over the plan, would make "a great prime minister".

Trump denied Friday that he had criticised May, suggesting that there was an element of "fake news" in the report -- even though The Sun released audio recordings confirming his words.

His interview drew outrage among British politicians, who accused him of being "determined to insult" May after 18 months of testy relations between the pair.

They also fired up demonstrators in London.

Chanting "No Trump, no KKK, no fascist USA!", they flew a huge balloon of the president depicted as a crying baby outside the Houses of Parliament.

Even Londoners not protesting and stopping to take in the mass of people, placards and sloganeering seemed supportive of the demonstrations.

"He brings it on himself -- it's like having a juvenile in charge of a superpower," said construction worker Dan Kelly, 47.

'Kill' trade plans

Less than nine months before it intends to leave the EU, the British government published its blueprint on Thursday calling for close trade ties with the bloc, outraging those who want a cleaner break.

In The Sun interview conducted Wednesday, Trump said he had advised May on the way forward but she had ignored him, adding that "it is too bad what is going on."

"The deal she is striking is a much different deal than the one the people voted on," in the 2016 EU referendum, he told the paper.

He warned staying close to the bloc "will probably kill" hopes of a British trade deal with the US.

His comments echoed the concerns of many Brexit supporters in her Conservative party, and fuelled talk of rebellion following the resignations of Johnson and Brexit secretary David Davis over the plan this week.

They also saw the value of the pound plunge on currency markets.

But Trump said Friday that after speaking with May's officials and trade experts that a deal between the two countries "will be possible", adding that Brexit presented an "incredible opportunity".

May added: "We agreed today that as the UK leaves the European Union, we will pursue an ambitious UK-US free trade agreement."

The two leaders also emphasised their continued cooperation on defence and security, after earlier watching a display of special forces from both countries at the military academy at Sandhurst.

Trump thanked the prime minister for her support at a testy NATO summit this week in Brussels, where he subjected America's other allies to a roasting over their defence spending.

Tough on Russia

Trump will spend the weekend at one of his Scottish golf courses before going to a summit in Finland on Monday between Trump and President Vladimir Putin.

May said they had agreed to engage with Russia with "strength and unity", and Trump said he has been "tougher on Russia than anybody".

Britain has accused Putin's government of unleashing a deadly nerve agent in the English city of Salisbury. Moscow denies the charge, but May is pressing Trump to raise the issue with Putin.

Trump has been accompanied on his trip to Britain by his wife Melania, who met veterans and schoolchildren in London on Friday along with May's husband Philip.

The American couple will later Friday take tea with Queen Elizabeth II at Windsor Castle.