Scandals, economic pain and an uproar over lockdown parties have left Britain’s Conservatives at risk of losing both recent advances and old strongholds.WAKEFIELD, England — Prime Minister Boris Johnson has yet to campaign in the stately but faded city of Wakefield in West Yorkshire, even though his Conservative Party is at risk of losing a highly symbolic seat in a parliamentary election there on Thursday. But that doesn’t mean he’s not on people’s minds — or tongues.“Boris Johnson has been convicted of breaking the law. He held parties in the place where they make the laws. It’s massive hypocrisy,” said Jordan Rendle, 31, who was getting his hair cut by a local barber, Andrew Prust.“We’re all human — 99.9 percent of the country didn’t stick to the rules,” Mr. Prust replied, his shrug reflected in the mirror.“OK, stop the haircut now!” Mr. Rendle spluttered in mock outrage, as he realized his barber backed the prime minister.“Boris Johnson has been convicted of breaking the law,” said Jordan Rendle, getting his hair cut, adding: “It’s massive hypocrisy.”Andrew Testa for The New York TimesEven in races where Mr. Johnson is not on the ballot, he manages to be an all-consuming, often polarizing figure. While this election, along with one in southwestern England, is to fill seats vacated by two lawmakers whose careers were ruined by their own scandals, the races are also a referendum of sorts on the scandal-scarred prime minister.How badly has he been damaged by the uproar over illicit parties held in Downing Street during the pandemic?Were the Conservatives to lose both seats, which is conceivable, it would do fresh damage to the record of electoral success that has helped Mr. Johnson survive the kind of turmoil — including a no-confidence vote by his own party — that would have sunk most politicians. A double defeat could trigger another mutiny among the 148 rebel Tory members of Parliament who voted to oust him only two weeks ago.“If those elections were to be lost quite badly, I can’t see why a good proportion of those M.P.s wouldn’t be demanding another no-confidence vote,” said Tim Bale, professor of politics at Queen Mary University of London. “By-elections have a nasty habit of making a generalized problem acute.”For all the high stakes, campaigning in Wakefield has been muted.Andrew Testa for The New York TimesPolls suggest the Conservatives are on track to lose Wakefield to the main opposition Labour Party, less than three years after they won it in Mr. Johnson’s 2019 election landslide. That would give Labour back a seat it held for nearly 90 years and restore a brick to the party’s “red wall” — areas in England’s equivalent of the rust belt, former industrial cities and towns that were once Labour strongholds.The election in Tiverton and Honiton, in the rural Tory heartlands to the south, is more of a tossup. There, the centrist Liberal Democrats are hoping to evict the Conservatives from a seat they held since the district was created in 1997, and won with a hefty margin in 2019.The incumbent, Neil Parish, resigned in April after he admitted watching pornography on his phone while sitting in the House of Commons. In Wakefield, the Conservative, Imran Ahmad Khan, was jailed after being convicted of sexually assaulting a teenage boy.Prime Minister Boris Johnson of Britain speaking in 2019 during his Conservative Party’s final election campaign rally in London.Kirsty Wigglesworth/Associated PressThe lurid circumstances that required these off-year elections makes the Conservative Party especially vulnerable. It adds to the perception of what critics call “Tory sleaze.” But there is deeper disillusionment with politics in Wakefield, where a strike at one of the bus companies has depressed business at shops and restaurants.“Politicians always make promises and then they always break them,” said Christine Lee, 82, a retired dress designer, as she browsed in one of Wakefield’s mostly deserted outdoor shopping malls. She said she did not plan to vote on Thursday because neither the Labour nor the Conservative candidate would make a difference.Given its high stakes, the campaign has been surprisingly muted. The Labour candidate, Simon Lightwood, who is comfortably ahead in the polls, has avoided making waves. His Tory opponent, Nadeem Ahmed, has gone quiet since he gave an ill-fated interview to The Daily Telegraph last week, in which he described his predecessor, Mr. Khan, as a “one bad apple,” who should not cause voters to turn against all Conservatives.A Labour stronghold in Wakefield. The party lost the seat in 2019, but has been ahead in polls there.Andrew Testa for The New York TimesDavid Herdson, who is running for the independent Yorkshire Party, left the Conservatives because of Mr. Johnson’s “reckless strategy” on Brexit.Andrew Testa for The New York TimesMr. Ahmed likened the case to that of Harold Shipman, a notorious English doctor and serial killer who is believed to have murdered 250 of his patients as a general practitioner before killing himself in prison in Wakefield in 2004. “Have we stopped trusting G.P.s?” Mr. Ahmed said to the Telegraph. “No, we still trust G.P.s and we know that he was one bad apple in there.”Mr. Johnson has so far kept his distance. On Friday, he skipped a conference of northern Conservative lawmakers in the nearby city of Doncaster, instead making a repeat visit to the Ukrainian capital Kyiv, where he met President Volodymyr Zelensky.To some local politicians, that was a telling sign.“Conservatives don’t think it’s worth fighting for,” said David Herdson, who is running for the seat as the candidate of the independent Yorkshire Party. “Labour thinks the election is in the bag, and they don’t want to make any mistakes.”Mr. Herdson, 48, who left the Conservative Party because of what he called Mr. Johnson’s “reckless strategy” in leaving the European Union, is emphasizing local concerns like affordable housing and better public transportation. He hopes for a respectable finish in the top five of a 15-candidate field. But in knocking on doors, he says he has encountered a “massive cynicism toward the political class in general.”A Labour Party spokeswoman, Phoebe Plomer, said Mr. Lightwood would spend the final days of the campaign telling voters that by defeating the Tories in Wakefield, they had a chance to force Mr. Johnson out of power. Under the rules of the Conservative Party, Mr. Johnson is not subject to another no-confidence vote for at least a year, though the rules can always be changed.A discount store in Wakefield, where a bus strike has emptied the town center.Andrew Testa for The New York TimesEither way, a loss in Wakefield would carry great symbolism. In 2019, the Conservatives pierced the red wall on the strength of Mr. Johnson’s promise to “get Brexit done.” That message appealed to disillusioned Labour voters, many of whom voted to leave the European Union in 2016. It was hailed as one of the most significant political realignments in British politics since the free-market revolution engineered by one of his Conservative predecessors, Margaret Thatcher.But instead of being revolutionary, Mr. Johnson’s leadership has been chaotic. In the wake of the no-confidence vote, his ethics adviser quit in despair last week, and Parliament is still scrutinizing whether the prime minister lied to lawmakers. On top of all that is a cost-of-living squeeze and a potential recession in the coming months.“There is this conventional thinking that Boris is this Heineken politician who can appeal to Labour voters,” Mr. Bale said, alluding to British ads in which a lager brand promised that it “refreshes the parts other beers cannot reach.”“But his appeal is actually kind of limited,” Mr. Bale said, “and he has become more of a liability then an asset.”Shoppers at an outdoor food market in Wakefield.Andrew Testa for The New York TimesGeoff Hayes, 72, who once worked in the now-defunct coal mines that ring Wakefield, said Mr. Johnson had sold many Labour voters on the promise that Brexit would liberate Britain from the regulatory shackles of the European Union. Now, however, they were realizing that the reality was trucks lined up for miles at ports on the English Channel, where they faced delays because of bureaucratic customs paperwork.“A lot of people thought Brexit was going to change everything,” said Mr. Hayes, as he gazed at peregrine falcons nesting in the steeple of Wakefield’s cathedral. “But in the end,” he said, “the Tories only care about the mega rich.” More