President Trump’s news conference in London on Tuesday with British Prime Minister Theresa May was supposed to underline how great a free-trade deal with the United States would be if Britain finally leaves the European Union.

Instead, Trump may have inadvertently played into some of Britons’ worst fears about their post-Brexit future when he suggested that Britain’s National Health Service (NHS) could be a part of a U.S.-Britain trade deal.

“When you’re dealing on trade, everything is on the table — so NHS or anything else, and a lot more than that,” the president said when asked about the position of Britain’s health system in a trade deal. “Everything will be on the table, absolutely.”

May, keenly aware of how sensitive an issue the NHS is in Britain, stepped in quickly, saying that “the point about making trade deals is that, of course, that both sides negotiate.”

Trump’s vague answer to the question may suggest he hadn’t given the idea much thought. He may already be reconsidering his position.

British journalist Piers Morgan wrote on Twitter earlier in the day that Trump had made a “stunning U-turn” on the issue in an interview conducted shortly after Tuesday’s news conference.

“I don’t see it being on the table,” Morgan quoted Trump as saying in the interview, which is due to be televised early Wednesday morning. “That’s something I would not consider part of trade. That’s not trade.”

Whether or not he later had a change of heart, Trump’s comments at the news conference Monday about the NHS have riled politicians on both sides of the aisle by touching on one of the most sacrosanct aspects of British life.

“Our NHS is not for sale,” Jeremy Corbyn, leader of the left-wing Labour Party, tweeted, later following up with a retweet of an edited video of Trump’s comments.

Shortly after Corbyn’s tweet, Dominic Raab, a member of the pro-Brexit wing of the governing Conservative Party, echoed the sentiment. “The NHS is not for sale to any country and never would be if I was Prime Minister,” tweeted Raab, who is a candidate to replace May as party leader.

Both Corbyn and Raab have a shot at being prime minister in the not-too-distant future, but they otherwise have little in common.

Corbyn is an old-school leftist who has spoke of renationalizing Britain’s water, electricity and gas systems. Raab, meanwhile, once appeared in a television interview with biographies of presidents Richard M. Nixon and Ronald Reagan gratuitously arranged on his window ledge.

That the two were apparently united over the NHS is significant. Founded in 1948, it is the largest single-payer health system in the world and primarily funded by the British government.

The behemoth system is simultaneously one of the most lauded and derided parts of British life. Polls have shown that the NHS is more cherished than the monarchy or the British army but also that many Britons are dissatisfied with the service and worried about its future.

Britain’s decision to leave the European Union has brought to light many problems with the NHS, including the possibility that the thousands of E.U. citizens who work for the institution may have to leave.

At the same time, claims that there would be a windfall in NHS funding with an end to contributions to the E.U. budget — $500 million a week, according to whose who campaigned to leave the bloc — have been debunked and disavowed.

Now there are fears that a trade deal with the United States could open up the NHS to profit-driven U.S. business interests — and with it, the creeping possibility of privatization.

“I think the entire economy, in a trade deal, all things that are traded would be on the table,” Woody Johnson, U.S. ambassador to Britain, said during an interview with the BBC on Sunday.

Would that mean health care? “I would think so,” Johnson responded.

The remark, like Trump’s comments at the news conference, sparked condemnation from British political figures. “My American friends, know this: The NHS is not for sale,” tweeted Matt Hancock, secretary of state for health and social care — and another candidate to replace May.

Both Trump and Johnson’s statements about the NHS and its potential role in trade talks have been vague. It’s also worth noting that U.S. firms are already involved in providing NHS services, some doing so in a private capacity within NHS hospitals.

Private involvement in the NHS has been growing for some time, and some fear that eventually the floodgates might open to a more profit-driven health system, if not a “Trojan horse” for a fully privatized system.

Trump’s rough-and-ready approach to trade negotiations will do little to calm these concerns. Nor will his past criticisms of the NHS.

In February 2018, he tweeted that thousands of people were marching in Britain because their universal health-care system was “going broke and not working.”

But Trump had badly misinterpreted the protests: They were, in fact, in support of the NHS and calling for greater government funding.