It is easy to say the wrong thing on a foreign visit, especially if you are President Donald Trump. It is even easier if you deal with your own lack of knowledge, as he does, by resorting to absolutes. On Tuesday, Trump appeared at a press conference with Theresa May, who is the Prime Minister of the United Kingdom but, thanks to a political crisis brought on by Brexit, won’t be for much longer. (She has said that she will step down as the Conservative Party leader on Friday, and then linger on, effectively as a caretaker Prime Minister, until a new leader is chosen, which is now due to happen by July 22nd.) Francis Elliott, a reporter for the Times of London, asked Trump if he agreed “that the entire economy needs to be on the table in a future trade talk, trade deal, including the N.H.S.?” Woody Johnson, the U.S. Ambassador to the United Kingdom and a co-owner of the Jets, had suggested in an interview that everything, including access to the health-care sector represented by the U.K.’s National Health Service, might be negotiable.

“I think we’re going to have a great trade deal, yes,” Trump began. “I think we’re going to have a great and very comprehensive trade deal.”

This was too vague for the British ear. Elliot interrupted him: “With the N.H.S.? Should the N.H.S. be on the table, sir?”

“I can’t hear him,” Trump said. “What?”

At this point, it appears to have occurred to May that Trump might not have grasped what the N.H.S.—which had been referred to only by its initials—was, let alone the attachment the British feel to a system that provides universal care, or the anxiety they have about its future. “It’s a question about the National Health Service,” she told the President. “He says, ‘Should the National Health Service be on the table?’ ”

Trump still didn’t seem to register her caution—or, more likely, just didn’t care. “Look, I think everything with a trade deal is on the table,” he said. “When you’re dealing in trade, everything is on the table. So, N.H.S. or anything else. There are a lot—a lot more than that. But everything will be on the table, absolutely.” It was as if he had lapsed into repeating a schoolyard riddle: Which came first—the trade or the table? And, in Britain, alarms started blaring. Did Trump want to somehow stick a big golden “T” on the N.H.S.?

“We welcome you as our guest to commemorate D-Day but don’t even think about doing deals with our beloved NHS . . . BUTT OUT, MR PRESIDENT,” a Daily Mail headline ran. The Guardian warned that Trump “EYES UP NHS.” “Theresa May stood next to @realDonaldTrump as he said the NHS will be ‘on the table’ in a US trade deal,” Jeremy Corbyn, the leader of the opposition Labour Party, tweeted. “And that’s what Tory leadership contenders and Farage are lining up for the No Deal disaster capitalism plans they have.” Corbyn added, “They all need to understand: our NHS is not for sale.” Nigel Farage is an icon of irresponsibility and the head of the new Brexit Party. The Tory “contenders” are myriad, and a number of them rushed to say that they were not about to mess with the N.H.S. Dominic Raab, a hard Brexiteer who wants May’s job, tweeted, “the NHS is not for sale to any country and never would be if I was Prime Minister.” Matt Hancock, another contender, tweeted, “Dear Mr President. The NHS isn’t on the table in trade talks - and never will be. Not on my watch.” And from Rory Stewart, a more moderate Tory, who also wants to be P.M., came: “In case there was any doubt - I would not be ‘offering up’ the NHS in any trade deal.” In Parliament on Wednesday morning, one of May’s ministers made it clear that she wouldn’t be, either.

That’s nice to know. But the levels of farce here are extraordinary. To begin with, the “trade deal” is an entirely notional construct, and will remain so for as long as the U.K. is part of the European Union, which negotiates on behalf of all twenty-eight of its member countries. And it still is. Brexit hasn’t happened yet, thanks to British squabbling and unwillingness to admit that certain promises about the benefits of Brexit that were made during the 2016 referendum on leaving the E.U. are lies—for example, that it would result in a windfall for the N.H.S. There is now an October 31st deadline. But, even under the withdrawal agreement that May negotiated with the E.U., it would be some time before the U.K. could negotiate its own deals. And, anyway, Parliament has rejected that agreement three times. A number of the alternative plans envision the U.K. remaining in a customs union with the E.U., which would take quite a lot of economic items off of the trade-deal table.

If, instead, the U.K. crashes out on Halloween with no deal, it will need a new trade deal with the U.S. in fairly short order. At that point, though, the threat to the N.H.S. won’t be that Trump and his American friends want their grubby hands on a national treasure. Rather, the threat will come from the uncertain status of E.U. citizens living in the U.K., who fill many of the jobs at the N.H.S., and from disruptions in the supply of pharmaceuticals and medical devices that are produced or rely on the E.U.’s regulatory framework, possibly leading to acute shortages and rising prices. In the longer term, the U.K. faces a loss of access to E.U. resources, including research institutions and financial backing, which nurture the health sector. Brexit is projected to make the U.K. poorer; that won’t help the N.H.S., either. Trump is a promoter and a magnifier of the forces that led to the victory of the Brexit side in the referendum. He is also a reminder of the economic vicissitudes that the E.U., to an extent, shields Europeans from. (“Disaster capitalism.”) The N.H.S. has also been vulnerable in recent years to austerity-spending drives and Tory calls for privatization. But Trump’s oafishness should not distract the U.K. from the fact that Brexit is its own problem.

Corbyn, meanwhile, addressed crowds who had gathered to protest Trump’s presence, and argued in defense of a strong N.H.S. But he has tried to play both sides of the Brexit question. (Corbyn also, clumsily, left it to Trump to let reporters know that he had asked for a meeting and that Trump turned him down.) The Tories, who are supposed to be governing, are consumed with their own delusions and appear desperate to do whatever it takes, no matter how bad it may prove for the country, to win back voters who defected to Farage’s Brexit Party in the recent European Parliamentary elections.

In the press conference, Francis Elliott, the Times reporter, had asked May if she would stay around long enough to negotiate such a trade deal with Trump. “Francis, nice try, but no. Look, I’m a woman of my word.” The leading contender to replace her, Boris Johnson, is not viewed as a man of his. Johnson, now a member of Parliament, was formerly the foreign secretary and remains a constant prevaricator. He is also an opportunistic Brexiteer. The President has said that he’s always liked him. Johnson, though, reportedly turned down a chance to meet with Trump, in favor of concentrating on leadership-fight machinations, but they spoke by phone. Trump did meet with Farage.

Another old friend whom Trump met in London was Piers Morgan, the journalist about town and former contestant on “Celebrity Apprentice.” Morgan interviewed Trump for the Wednesday-morning edition of the ITV show “Good Morning Britain,” where he asked if the N.H.S. really had to be part of a trade deal. “I don’t see it being on the table,” Trump said, with a shrug. “Somebody asked me a question today, and I say everything is up for negotiation, because everything is. But I don’t see that being—that’s something that I would not consider part of trade. That’s not trade.” Now he tells them. Morgan also gave Trump a gift: a hat like the one that Winston Churchill wears in several famous photos. “I’ll try it,” Trump said, and, for a moment, under its British brim, he seemed to disappear.