Mrs. May was challenged over her change of heart on several issues, including an abrupt shift last week over plans to finance long-term care, and the merits of “Brexit,” Britain’s withdrawal from the European Union — which she once opposed but now embraces. She was also pressed by members of a studio audience about cuts to financing for the police, health and education.
Mr. Corbyn, while outperforming relatively low expectations, appeared vulnerable when questioned about his willingness to authorize military force, his past opposition to the Falklands war in the early 1980s, and his expressions of regret that Osama bin Laden had been killed, rather than arrested and tried.
Television debates rarely affect the outcome of British elections, according to analysts, but this event gave Mrs. May a chance to reboot her lackluster campaign after the Manchester bombing last week, which prompted the suspension of electioneering for several days.
The attack itself was barely mentioned on the program, though Mr. Corbyn was challenged over his comments that the war on terrorism was not working, while Mrs. May was called out over cuts in the police ranks, even as she argued that spending on counterterrorism had increased.
Mrs. May’s shaky campaign and the tightening polls have undercut assumptions that she will win a resounding victory, but she is still expected to increase her narrow majority in Parliament.
Her campaign stumbled when she was forced to revisit a plan to put a hard cap on the assets that residents who receive long-term care at home may own.
The proposal, widely derided as a “dementia tax,” raised sufficient enough protests that Mrs. May beat a hasty retreat, even as she insisted that nothing had changed in her thinking. During Monday night’s debate, Mrs. May said there would be an absolute limit on the amount people would have to pay, but did not specify what it would be.
The furor over long-term care and her obvious change of heart over Brexit, which she had originally opposed, have dented her claims that only she can provide the “strong and stable” leadership Britain needs as it faces very difficult negotiations over how to extract itself from the European Union.
Mrs. May called the snap election for June 8, expecting to increase her parliamentary majority before the talks with Europe begin.
But Mr. Corbyn’s left-wing agenda has proved more popular than some had expected, despite questions about how it would be financed. He has also benefited from rules that, during election campaigns, oblige Britain’s broadcasters to balance the airtime given to the different parties, something that normally increases the visibility of the opposition.
Mr. Paxman provoked laughter from the studio audience, and a fierce stare from Mrs. May, when he suggested that during the Brexit negotiations, her European interlocutors would conclude that she was a “blowhard who collapses at the first sign of gunfire.”
She repeated her insistence that no Brexit deal with the European Union would be better than a bad deal. Mr. Corbyn argued that he would reach an accord allowing tariff-free trade with the European Union to continue despite his promise for “managed migration.” He said that he expected that immigration “would probably come down” but gave no estimates on numbers.
Despite her recent difficulties, Mrs. May also has some solid reasons to be content. The Liberal Democrats, the most pro-European of the parties, have so far failed to convince the millions of voters who opposed Brexit that they offer a viable alternative.
And the right-wing, populist U.K. Independence Party appears to be in its death throes — with its main policies of quitting the European Union and curbing immigration now appropriated by the Conservatives.
That leaves Mrs. May in a straight fight with Mr. Corbyn, which most analysts still expect her to win.