LONDON — President Trump on Tuesday urged Britain to forge ahead with plans to quit the European Union, reiterating his support for Brexit at a time of acute political crisis, as the prospect of a Britain overly dependent on the United States divided politicians and further inflamed thousands of anti-Trump protesters on the streets.
Mr. Trump dangled the prospect of a “phenomenal” trade deal with the United States if Britain breaks from Europe. But he made clear that in negotiations for such a deal, “everything will be on the table,” including opening Britain’s public health system to American competitors.
Taking credit for having predicted the outcome of Britain’s referendum in 2016, Mr. Trump said he believed Britain could now leave the European Union, even if it fails to make a deal with Brussels by the Oct. 31 deadline.
“I would think that it will happen, and it probably should happen,” Mr. Trump said at a news conference with Prime Minister Theresa May, who will step down as leader of the Conservative Party this week after having repeatedly failed to win approval in Parliament for her negotiated exit agreement.
“This is a great, great country and it wants its own identity,” said Mr. Trump, who had warm words for Mrs. May, even as he repeated that he would have taken a harder line than her in the talks with the European Union.
Relaxed and agreeable on the second day of his state visit to Britain, both in public and in his private meetings, Mr. Trump still seemed on a high after a day of circulating between palaces and mingling with royalty.
If the first day of Mr. Trump’s visit showcased a royal family determined to nurture the “special relationship” with the United States — lavishing their guest with a gilded banquet and a royal cannon salute — Tuesday plunged Mr. Trump into the murkier crosscurrents of British politics, where he remains deeply unpopular.
It also demonstrated, yet again, Mr. Trump’s penchant for barging into the most sensitive political debates of other countries — often turning himself into a lightning rod, which poses challenges for his allies and adversaries alike.
Boris Johnson, a pro-Brexit politician and former foreign secretary who is running to replace Mrs. May as the Conservative leader, spoke to Mr. Trump for 20 minutes by phone but declined a face-to-face meeting, citing a busy schedule as he prepares his campaign to replace Mrs. May. She will remain a lame-duck prime minister until the Conservatives elect her replacement this summer.
To many in Britain, Mr. Trump appeared less a friend tossing a lifeline than an opportunist angling to exploit Britain’s estrangement from Europe by pursuing a trade deal that would crack open Britain’s health service and foist chlorinated American chicken on British shoppers.
“This orange blow-in is brashly telling us how to conduct our own international affairs,” wrote Zoe Williams, a columnist at the Guardian, “and listening to him it is clear that a close relationship with Trump’s America would be as far removed from regaining sovereignty as it is possible to imagine. Allied to Trump, we’d be more of a satrapy than a nation state. We would be dominated by a power that was as raw as it was distant.”
Jeremy Corbyn, the leader of the opposition Labour Party, echoed those themes in a speech to anti-Trump demonstrators. He condemned Mr. Trump’s war of words with the mayor of London, Sadiq Khan, and warned that a trade deal with the United States would amount to “offering up our precious National Health Service to private American companies.”
“We will not stand for that,” Mr. Corbyn thundered to a crowd that waved placards with the slogans, “No Brexit. No Trump” and “Brexit = Trump.”
Demonstrators thronged Trafalgar Square and the surrounding streets, massing under the familiar sight of an orange blimp depicting a baby Trump clad in a diaper. A group of women marched in the red uniforms from Margaret Atwood’s novel of oppression, “The Handmaid’s Tale.” Others rallied around a statue that depicted Mr. Trump tweeting while seated on a golden commode.
The protesters divided into groups depending on their grievances: some attacked Mr. Trump on climate change, others on his Venezuela and Middle East policies. But on a rainy day, the turnout appeared smaller than during the president’s last visit to Britain in 2017. Mr. Trump insisted that cheering crowds lined the route of his motorcade and claimed, falsely, that reports of demonstrators were “fake news.”
“I heard there were protests,” Mr. Trump said. “I said, ‘Where are the protests? I don’t see any protests.’ ”
As for Mr. Corbyn, the president said the Labour leader had sought a meeting with him, but that he refused. “He is, where I come from, somewhat of a negative force,” Mr. Trump said.
He repeated his critique of Mayor Khan, whom he called a “stone cold loser” on Monday, shortly before landing in London. “He’s been a not very good mayor,” the president said. “Crime is up, lot of problems.”
Still, for this president, it was a restrained performance.
Mr. Trump praised Mr. Johnson, despite the fact that he turned down a meeting with Mr. Trump even after the president had promoted him as a successor to Mrs. May before the trip. Mr. Trump was expected to meet Michael Gove, the environment secretary and a rival of Mr. Johnson’s who is competing for the leader’s post.
“I know Boris; I like him. I’ve liked him for a long time. I think he’d do a very good job,” Mr. Trump said, adding, “I don’t know Michael.”
The president also met with Nigel Farage, the fiery leader of a pro-Brexit party. Mr. Farage was photographed entering Winfield House, the residence of the American ambassador. Afterward, he tweeted, “Good meeting with President Trump — he really believes in Brexit and is loving his trip to London.”
For Mrs. May, who worked for many months to arrange Mr. Trump’s state visit, it was a more bittersweet occasion. She and her husband, Philip, greeted Mr. Trump and the first lady, Melania, outside 10 Downing Street and gave them a tour of Britain’s most famous political address — one that she will soon vacate. After the news conference, the two couples toured the Churchill War Rooms museum.
But Mr. Trump resisted taking another shot at his host, whom he faulted last year for not negotiating aggressively enough with the European Union. The two leaders have often seemed uncomfortable in each other’s presence. But at their final news conference, there was something approaching warmth.
“I seem to remember the president suggested that I sue the European Union,” Mrs. May said, casting a playful glance at Mr. Trump. “Which we didn’t do. We went into negotiation and we came out with a good deal.”
“I would have sued, but that’s O.K.,” Mr. Trump replied with a smile. “I would have sued, and maybe settled, maybe.”
The president hastened to add, “She’s probably a better negotiator than I am,” and said Mrs. May’s negotiations might have teed up a deal with the European Union. Mr. Trump often takes maximalist positions — like threatening to rip up the North American Trade Agreement — as a precursor to further deal-making.
“Perhaps you won’t be given the credit you deserve if they do something,” Mr. Trump said to Mrs. May. “But I think you deserve a lot of credit, I really do.”