Trump lobs Brexit grenade at UK Prime Minister Theresa May

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 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.

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

"She should negotiate the best way she knows how. But it is too bad what is going on," the president said.

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 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.

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.

"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.

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

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

In another blow to May, Trump said her now ex-foreign secretary "would be a great prime minister. I think he's got what it takes."

May and Trump are scheduled to hold talks and a joint news conference on Friday.