He told The Sun tabloid it was not what Britons backed when they voted in a June 2016 referendum to quit the European Union.
In an interview conducted before he began his visit, which will draw large protests, Trump said May's plans for close future ties with the EU would "probably kill" her hopes for a trade deal with the United States.
He told The Sun tabloid it was not what Britons backed when they voted in a June 2016 referendum to quit the European Union, and also said former foreign minister Boris Johnson, who resigned this week over the Brexit plan, would make "a great prime minister".
Junior British foreign minister Alan Duncan sought to brush off the remarks, telling BBC radio: "Donald Trump is a controversialist, that's his style... I don't think we see it as rude."
But the comments drew outrage from some British lawmakers and will make for an awkward atmosphere with May when the pair meet at her country retreat of Chequers for a working lunch, followed by a press conference.
They also undermine the prime minister as she faces speculation of a leadership challenge from eurosceptics in her Conservative party following the resignations of Johnson and Brexit secretary David Davis.
Trump, a long-time supporter for Brexit, said he had advised May to leave the EU in a different way but was ignored.
"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," he told The Sun.
"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."
Referring to the Brexit blueprint published by the government on Thursday, which calls for close trading links with the EU after Brexit, Trump said: "The deal she is striking is a much different deal than the one the people voted on.
"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."
Duncan suggested the president had not seen the detail of the plan when he gave the interview on Wednesday, while also stressing that the much-vaunted special relationship was about much more than Brexit.
But Anthony Gardner, who was former president Barack Obama's ambassador to the EU, held nothing back in attacking Trump's attack on May as "totally unacceptable" and "unprecedented" in the middle of a high-profile visit.
"He is out of control and an embarrassment. He is (a) one-man wrecking machine," Gardner tweeted.
Trump flew into Britain on Thursday, having already subjected NATO allies in Brussels to a roasting over their levels of defence spending.
May has insisted that her Brexit plan will allow Britain to strike its own lucrative trade deals with countries like the US after leaving the EU in March next year.
She pressed Trump about the deal on Thursday at a gala dinner at Blenheim Palace, the birthplace of Britain's World War II leader Winston Churchill.
Brexit "creates an opportunity to reach a free trade agreement that creates jobs and growth here in the UK and right across the United States", she said.
But Trump poured cold water on May's offer.
"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," he said.
White House spokeswoman Sarah Sanders later told reporters Trump was "thankful for the wonderful welcome" he received in Britain.
"The president likes and respects Prime Minister May very much. As he said in his interview with The Sun she 'is a very good person' and he 'never said anything bad about her'," she said.
Trump and May are due to watch a display of military special forces on Friday before their formal talks which will cover Russia, ahead of a summit in Finland on Monday between Trump and President Vladimir Putin.
Putin's government is accused by May's 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 will later Friday take tea with Queen Elizabeth II at Windsor Castle, before spending the weekend in Scotland on a private visit that will likely take in 18 holes at one of the property magnate's golf courses, where more protesters await him.
He will not attend any high-profile events in London but a mass protest is planned in the capital on Friday, where demonstrators will fly a giant balloon next to the British parliament depicting Trump as a nappy-clad baby.
The balloon was authorised by London Mayor Sadiq Khan, who has crossed swords with Trump several times after the president posted factually incorrect messages over a series of terror attacks in Britain in 2017.