Mays greets Trumps for UK black-tie dinner
Donald Trump has said the UK will "probably not" get a trade deal with the United States, if the prime minister's Brexit plan goes ahead.
He told The Sun the PM's plan would "probably kill the deal" as it would mean the United States "would be dealing with the European Union" instead of with the UK.
Theresa May has been making the case for a US free trade deal with Mr Trump, on his first UK visit as president.
She said Brexit was an "opportunity" to create growth in the UK and US.
Mr Trump and the first lady were given a red carpet reception at Blenheim Palace, Oxfordshire on Thursday evening.
He was at a black-tie dinner with Mrs May as news broke of his interview with the newspaper.
Mr Trump told The Sun that the UK's blueprint for its post-Brexit relations with the EU was "a much different deal than the people voted on".
On the subject of a future trade deal, he said the Chequers deal would mean it would be "most likely ... we would be dealing with the European Union instead of dealing with the UK, so it will probably kill the deal".
He said he had told Mrs May how to do a Brexit deal, but: "She didn't agree, she didn't listen to me."
"I told her how to do it. That will be up to her to say. But I told her how to do it. She wanted to go a different route," he said.
The United States president also said he was "cracking down" on the EU because "they have not treated the United States fairly on trading".
On Thursday, the UK government published its plan for its long-term relationship with the EU.
It hopes the EU will back the proposals so an exit deal can be struck by the autumn, ahead of the UK's official departure from the EU in March next year.
The long-awaited White Paper is aimed at ensuring trade co-operation, with no hard border for Northern Ireland, and global trade deals for the UK.
But leading Brexiteers, Boris Johnson and David Davis, resigned from the cabinet days after ministers reached agreement on the plan at Chequers a week ago.
Mr Johnson launched a scathing attack on the PM's strategy, saying the "dream is dying, suffocated by needless self doubt". Another leading Tory rebel, Jacob Rees-Mogg, described it as a "bad deal for Britain".
Responding to an earlier suggestion by President Trump that the British people were not getting the Brexit they voted for, Mrs May said: "We have come to an agreement on the proposal we are putting to the European Union which absolutely delivers on the Brexit we voted for.
Analysis, by BBC political editor Laura Kuenssberg
From the moment of his election, Donald Trump was an awkward friend for Theresa May.
He runs towards a fight. She does everything in public to avoid one.
Well, just before they were due to appear alongside each other on UK soil he publicly, and at length, gave a "both barrels" verdict on her most important policy.
Read more from Laura
"They voted for us to take back control of our money, our law and our borders. That is exactly what we will do."
Mr Trump's visit comes as the government published its plans for the UK's relations with the EU after Brexit.
Earlier this week he said it was "up to the people" whether the prime minister stayed on after two cabinet ministers resigned over her Brexit policy.
At the dinner, Mrs May stated that more than one million Americans work for UK-owned firms, telling Mr Trump: "As we prepare to leave the European Union, we have an unprecedented opportunity to do more.
"It's an opportunity to reach a free trade agreement that creates jobs and growth here in the UK and right across the United States.
"It's also an opportunity to tear down the bureaucratic barriers that frustrate business leaders on both sides of the Atlantic.
"And it's an opportunity to shape the future of the world through co-operation in advanced technology, such as artificial intelligence."
US President Donald Trump arrived at Stansted Airport for a two-day working visit
The Trumps landed at Stansted Airport, Ess3x, at 13:50 BST before a helicopter took them to Winfield House in Regent's Park, where they are staying as guests of the United States ambassador.
They stayed there for several hours before travelling to the 18th Century palace near Woodstock for the evening's events.
As Mr Trump arrived in the UK, protesters gathered outside the United States ambassador's residence in London, and an estimated 1,000 of them demonstrated near the palace, the birthplace of wartime Prime Minister Winston Churchill.
John Rees of the Stop the War group addressed protesters, saying of Trump: "He's a wrecking ball for race relations, he's a wrecking ball for prosperity, he's a wrecking ball for women's rights, he's a wrecking ball for any peace and justice in this world and we have to stop him."
The president briefly held Mrs May's hand as they walked up the stairs to the palace, in a repeat of her visit to the White House when they held hands for a short time.
Business leaders from sectors including finances, travel, food and defence were among the guests at dinner.
Cabinet ministers including the newly-appointed Foreign Secretary Jeremy Hunt and Chancellor Philip Hammond were also present.
They were entertained by The Countess of Wess3x's Orchestra, playing British and American hits of the 20th Century during dinner.
Only one person, the digital entrepreneur and philanthropist Baroness Martha Lane-Fox, has publicly refused the invitation.
They were given a best-of-British dinner, featuring Scottish salmon, Hereford beef fillet and strawberries with clotted cream ice-cream.
During the dinner, Mrs May stressed that the United States and UK are "not just the closest of allies, but the dearest of friends".
Some of Mr Trump's supporters and protesters have been explaining their motivation
On Friday, Mrs May and Mr Trump will go to watch a joint counter-terrorism exercise by British and US special forces at a military base.
The pair will then travel to Chequersthe PM's country residence in Buckinghamshirefor talks with the foreign secretary.
Extra security is in place to police the protests. More are planned for the second day of Mr Trump's visit.
The president and first lady will travel to Windsor on Friday afternoon to meet the Queen, before flying to Scotland to spend the weekend at Mr Trump's Turnberry golf resort. This part of the visit is being considered private.