COVENTRY, England — Along with millions of Britons, Jules Barcroft bought into the bold promise made by Boris Johnson in the 2016 Brexit campaign: that leaving the European Union would bring buckets of new money into the long starved National Health Service.
So she voted for Leave, staking her own health — she has multiple sclerosis and lifelong diabetes — on that pledge by Mr. Johnson, now the prime minister.
Three years later, however, she feels used.
“That was all a lie,” Ms. Barcroft said. “Why would they look after our medical needs? That’s not high on their agenda at all.”
With Britain on the precipice of an election that could soon lead to a decisive break with the European Union, Brexit looks to many people more like a threat to their cherished health service than its salvation. The system has already deteriorated under the watch of Mr. Johnson’s Conservative Party, with beds overflowing, waiting times swelling and nurse and doctor vacancies piling up.
In recent days, the growing strains on the National Health Service jolted the campaign as some hospitals buckled under wintertime demands, and an irritated Mr. Johnson struggled to respond.
The problems vindicated a drumbeat of warnings from the Labour Party that Mr. Johnson was undermining Britons’ health care for Brexit.
And they created a potent threat to Mr. Johnson’s campaign in the waning days of an otherwise sluggish race. It did not help matters that, shown a picture during a television interview on Monday of a 4-year-old boy lying on the floor of an overcrowded hospital, Mr. Johnson at first refused to look.
Instead he repeated Brexit talking points, leaving many with a lasting image of the sort of icy, oblivious lawmaker who represents what swing voters fear most about the Conservatives’ record on public services.
The Conservatives have a healthy lead in national polls, but that disguises considerable uncertainty in dozens of hotly contested seats, making any missteps by Mr. Johnson significant as Labour tries to close the gap. Mr. Johnson, using the tactics of the 2016 Brexit campaign, has tried to inoculate himself by rebranding the Conservatives as the protectors of the health service, though not without some controversy.
He recently had to acknowledge that a pledge for 50,000 more nurses included funding for only 31,000 new recruits. Similarly, after Mr. Johnson announced plans to build 40 new hospitals around the country, it became clear that the government was giving the money to six hospitals to upgrade existing buildings.
But that has not stopped Mr. Johnson from writing a stream of Twitter posts about the health service and visiting hospitals with promises of better primary care and new equipment. The efforts may have paid off: Some polls show that Mr. Johnson is now more trusted than the Labour leader, Jeremy Corbyn, to take care of the health service.
But the challenges to the health service will continue after the election on Thursday — all the more so if the result leaves Britain heading toward contentious post-Brexit trade negotiations with the United States.
President Trump, as part of his “America First” agenda, has vowed to make foreigners pay more for American-produced pharmaceuticals. Britain, desperate for a post-Brexit trade deal with the United States, would be susceptible to requests that it drop its stranglehold on drug prices, trade experts say.
At the same time, pressure on the health service has been building since the Conservatives came to power in 2010 and trimmed annual budget increases during a long period of austerity.
Hospital waiting times reached record highs in October, with one in six people who visited emergency departments in England waiting longer than four hours to be seen. The number of people on hospital waiting lists has ballooned to nearly five million.
And now the health service is going into winter — a particularly busy period for hospitals — while dealing with a pension crisis, bed shortages and the prospect of a major flu outbreak. Medical chiefs are concerned about how they will cope.
“I would say that in the last five to six years, I haven’t seen confidence levels this low heading into winter,” said Siva Anandaciva, a chief analyst at The King’s Fund, a health care charity.
Ms. Barcroft lives in the Coventry area, a pocket of working-class Labour strongholds in central England being targeted by Mr. Johnson, and she is one of many voters for whom the health service has become the dominant issue in the days leading up to the election. Some polls show that the health service is neck and neck with Brexit as the most important issue to potential voters.
For Labour, success on Election Day is dependent in large part on whether it can pull the focus from Brexit and make a case that Mr. Johnson would squander precious public services.
The party has pledged to outspend the Conservatives by pumping an additional 26 billion pounds, or about $34 billion, into the health service annually by 2024. Eager to hold onto its mantle as the party of the National Health Service, Labour has also vowed to undo shifts in recent decades toward privatization — a move that would entail a major reorganization of the health service.
A Labour supporter for most of her life, Ms. Barcroft is sympathetic to Mr. Johnson’s message that Britain needs to get Brexit done, despite her misgivings about voting for it in 2016. But since then, she has also dealt with the ravages of an overburdened health service working under the cloud of Brexit.
Ms. Barcroft, a Type 1 diabetic, has had to keep a stock of out-of-date, secondhand insulin in her fridge, just in case a disorderly Brexit suddenly chokes off her usual supply.
With the major insulin manufacturers all in continental Europe, diabetes patients have pushed for guarantees that they will be able to refill prescriptions if Britain leaves the European Union without a deal managing future relations.
Some patients say they have ordered extra insulin to protect against a no-deal Brexit. Others started buying blood monitoring equipment on Amazon or stocking up on other patients’ leftover supplies, as Ms. Barcroft has done.
“I do feel a bit like I’ve got to look after myself here,” she said.
Ms. Barcroft also said her regular nurses were often missing from her monthly infusion treatments for multiple sclerosis. Nearly 5,000 nurses from European Union countries have left the British health service since the Brexit referendum, part of an exodus of more than 10,000 European workers who were once a mainstay of the health service staff.
And some facilities have flatly refused to give Ms. Barcroft her regular medications on the grounds of cost, she said, adding that one doctor had pulled out a book of drug prices to explain why she could not be given her multiple sclerosis infusions in that area. The doctor suggested she take steroids instead.
“I came out of there and I just thought, ‘Oh my god, I am such a burden on the N.H.S.,’” Ms. Barcroft said. “He literally spelled out to me how much money I was costing the N.H.S. I just felt like I’m a drain on resources.”
She said the experience had left her unable to support the Conservatives, but she also had deep reservations about Mr. Corbyn’s leadership. In the days before the election, she doubted that she would vote at all.
Trade experts say drug prices could rise further after Brexit. Mr. Trump said this summer that the health service would be “on the table” in trade talks, before later backtracking on that claim amid efforts to protect Mr. Johnson, an ally, from criticism.
But government documents recently circulated by the Labour Party (and initially posted online by an account linked to a Russian campaign) indicated that American trade negotiators saw British drug prices as a “key consideration going forward.”
For a country that has not negotiated its own trade deals in decades, the risks to the health service have driven home the fact that Britain will not always get its way on the world stage, said Tom Kibasi, a left-wing policy analyst who once worked for the chief executive of the National Health Service.
“It’s just dawning on the public that this idea of a trade deal is not as one way as they think it is,” Mr. Kibasi said. “People know when there is a limited N.H.S. budget, if the U.S. forces higher prices onto the U.K. as part of a trade deal, that means less money for other services. The threat is about selling out the N.H.S. to get a deal with Trump.”