He added: "We have enough difficulty with the European Union".
"If signing up to the Trump worldview is the price of a deal, it's not worth paying".
"We agreed today that as the United Kingdom leaves the European Union we will pursue an ambitious U.S. -UK free trade agreement", she said. Protesters against Trump's visit gather near an entrance to the USA ambassador's residence in Regent's Park in London on Thursday.
But the US President seemed to be visibly annoyed when he was asked by a reporter if he regretted making remarks about British Prime Minister Theresa May and her Brexit policy in an explosive interview.
"If he actually says these things standing next to her [at the press conference], then basically she's toast in terms of the plans that she now has", he said, adding that May is already under "enormous pressure" from her partymates, who are against her deal with the EU.
"I would have done it much differently".
Trump's comments were condemned by British politicians as it delivered an astonishing political knifing of the already embattled May, comprehensively undermining her fragile position in Britain's tortuous negotiations on leaving the European Union next year.
"I actually told Theresa May how to do [Brexit], but she didn't listen to me", Trump said in the Sun interview, and then mused that May's Conservative Party rival, Boris Johnson, "would be a great prime minister".
"I would say I would give our relationship in terms of grade the highest level of special", Mr Trump said.
Think your friends would be interested? "He obviously likes me and says very good things about me", he added.
Mr Trump went further and suggested to the Sun Mr Johnson was "a great representative for your country".
Donald Trump arrives in Britain on Thursday for his first visit as United States president, flying into a whirlwind of protests. "But when they make you feel unwelcome, why would I stay there?"
"I used to love London as a city", Trump said. I haven't been there in a long time. "I think you are losing your culture".
In contrast to the president's sharp words, Trump's first event in England was an oasis of warm greetings at an evening reception Thursday at Blenheim Palace, birthplace of Winston Churchill, the larger-than-life British leader cited by the president as a model of leadership.
Trump even took a shot at London Mayor Sadiq Khan for not taking a harder line on immigration and painted the city as a hub for terrorism. Look at what is going on in London. "I get along with her very nicely", Trump said.
"I cherish the special relationship with the U.S. and the many Americans who contribute to our city", posted Khan, London's first Muslim mayor. I get along with her very nicely.
The President said the newspaper didn't include the "tremendous things" he said about Ms May in the interview.
Ms May also thanked the US President for his support over Russia, which Britain has blamed for a nerve agent attack on a former Russian spy in south-west England in March.