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

The interview was done while Trump was in Brussels for a contentious NATO summit and has drawn strong condemnation from British MPs with one accusing the president of disrespecting the UK while here on his first official visit.

Clearly siding with Brexiteers Trump told the newspaper that May's proposal risked future UK-US trade deals.

"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.

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

Trump told the Rupert Murdoch-owned newspaper he had advised May on how to conduct Brexit negotiations, "but she didn't listen to me" and in doing so had put trade negotiations with the US in peril.

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

Trump's comments came as May released long-awaited post-Brexit proposals which include keeping Britain and the EU in a free market for goods, with a more distant relationship for services, when they split next year.

The move has infuriated fervent Brexit supporters while Foreign Secretary Boris Johnson and Brexit Secretary David Davis quit in protest.

In a further blow Trump said Johnson "would be a great prime minister. I think he's got what it takes."

May and Trump are scheduled to hold talks on Friday.

Conservative MP Sarah Wollaston hit out at Trump on Twitter.

"The divisive, dog-whistle rhetoric in his @TheSun interview is repulsive," she tweeted on Thursday.

"If signing up to the #Trump world view is the price of a deal, it's not worth paying."

May insists her plan is what Britons voted for in 2016.

Australian Associated Press