US President Donald Trump has lobbed a verbal hand grenade at Theresa May saying the British PM has wrecked the UK's exit from the European Union and killed any chances of a free trade deal with the US.

Trump's comments were published in UK tabloid The Sun as Theresa May hosted the president and his wife Melania at an elaborate black tie welcome dinner at Blenheim Palace outside London.

Trump was interviewed by The Sun on Thursday when he was in Brussels for a contentious NATO summit before departing for the UK on his first official visit with Theresa May, who is keen to talk up a trade deal.

Tomorrow's front page: Donald Trump @realDonaldTrump accuses the PM of wrecking Brexit - and warns she may have killed off any chance of a vital US trade deal - full story HERE at 11pm https://t.co/JRrMjQDTBq pic.twitter.com/udCjYWQeeQ — The Sun (@TheSun) July 12, 2018

Trump told the Rupert Murdoch-owned newspaper he had advised May on how to conduct Brexit negotiations, "but she didn't listen to me."

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"I would have done it much differently. I actually told Theresa May how to do it but she didn't agree, she didn't listen to me. She wanted to go a different route.

"I would actually say that she probably went the opposite way. And that is fine. She should negotiate the best way she knows how. But it is too bad what is going on," he told the tabloid.

Trump's Brexit comments came on the same day May's government published long-awaited proposals for Britain's relations with the EU after it leaves the bloc next year.

"The deal she is striking is a much different deal than the one the people voted on," he said.

read more Donald and Melania Trump ready for tea with the Queen

The Brexit document proposes keeping Britain and the EU in a free market for goods, with a more distant relationship for services.

This has infuriated fervent Brexit supporters, who think it would limit Britain's ability to strike new trade deals around the world. Foreign Secretary Boris Johnson and Brexit Secretary David Davis both quit the government this week in protest.

"It was not the deal that was in the referendum. I have just been hearing this over the last three days. I know they have had a lot of resignations. So a lot of people don't like it," Trump said.

Trump also said former foreign minister Boris Johnson would make "a great prime minister".

He added London mayor Sadiq Khan, who has allowed protesters to raise a giant diaper-clan balloon mocking the US president next to parliament on Friday, was doing "a terrible job" on crime.

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Trump has sided firmly with Brexiteers, saying what May proposed would hurt the chances of a future trade deal between the UK and the US.

read more Hunt replaces Johnson as UK foreign secretary in Brexit fallout

"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 said.

May insisted earlier Thursday that her plan was exactly what Britons had voted for in the 2016 referendum.

Trump's comments will plunge the transatlantic "special relationship" to new lows, making for extremely awkward talks with May.