LONDON — In Prime Minister Boris Johnson’s telling on Tuesday night, Brexit was simple, a speed bump on the road to British prosperity.

But in the eyes of the Labour Party leader, Jeremy Corbyn, it was anything but, opening the door to a decade of tortuous trade talks and a sell-off of Britain’s cherished public services.

Those clashing messages, delivered to occasional groans from a studio audience Tuesday night, formed the core of the first debate before Britain’s general election next month, one that could determine whether Britain leaves the European Union or stays.

The argument befit an election consumed less by the merits of Brexit than by how painlessly Britain can move beyond it.

Mr. Johnson hammered again and again at the need to “get Brexit done,” casting it as the first step to solving everything from climate change to an erosion of trust in British democracy. Mr. Corbyn, on the other hand, refused to say even whether he wanted Britain to quit the European Union — arguing instead that the least disruptive way forward was returning the choice to Britons in a second referendum.

In a campaign that has seemed stuck in neutral, with Mr. Johnson’s Conservative Party holding a steady lead and Britons irritated by both main candidates, some analysts said that simply holding his own gave Mr. Corbyn a chance to turn the tide. But with Labour lawmakers antsy that their party is running out of time to close a double-digit polling deficit, it was not clear whether it would be enough.

Mr. Johnson is banking on Britons being so weary of a logjam in Parliament over Brexit that they overlook Mr. Corbyn’s criticisms and give Mr. Johnson the majority to push through his exit agreement. That deal made only halting progress in Parliament last month.

“Whether you voted for Leave or Remain, people want to get Brexit done, and to unleash the potential of this entire country,” Mr. Johnson said. “We have a deal that is oven-ready.”

Though the audience grew audibly annoyed with Mr. Johnson’s recurrent pleas to “get Brexit done,” the message makes up a big part of his appeal in a country that has watched lawmakers argue over the issue for three years, to little effect.

Likewise, Mr. Johnson tugged incessantly at one of Mr. Corbyn’s biggest vulnerabilities: his refusal to say whether he would campaign for Leave or Remain in a second referendum. At a moment when nearly all Britons seem to have made up their minds on Brexit, Mr. Corbyn’s silence has generated mistrust among anti-Brexit voters, even if Labour has clearly articulated its preference for a second public vote.

Mr. Corbyn, who is trying to hold together a coalition that includes both Leavers and Remainers, grew most passionate discussing Britain’s National Health Service.

Brandishing documents that he said described secret government meetings with American trade negotiators, Mr. Corbyn accused Mr. Johnson of wanting to “sell our National Health Service to the United States” during discussions over a post-Brexit free trade agreement.

And he briefly quieted a restive audience by telling the story of a friend who he said had died the day before of breast cancer after waiting eight hours for help.

“The N.H.S. is a wonderful and brilliant institution, but it is suffering under the most incredible pressure,” Mr. Corbyn said, citing thousands of nursing vacancies and long waits in emergency departments.

Labour trails by an average of roughly a dozen percentage points in polls, with Mr. Corbyn garnering the worst popularity ratings of a major party leader heading into a British election since the data was first tracked 40 years ago.

Hopes that Labour could repeat its dramatic comeback in the 2017 general election — perhaps with the rollout of its policy proposals this week — are fading as the party has failed to make up ground.

And the Liberal Democrats — a centrist party that wants to revoke Brexit altogether and could hurt the Conservatives in some seats — are struggling, too.

Tuesday night’s televised debate, still a relatively new element in British elections, featured a few stinging one-liners.

“A money forest, he’s got,” Mr. Johnson said of Mr. Corbyn’s big spending plans.

But Mr. Corbyn was also ready when Mr. Johnson warned of a “chaotic coalition” between Labour and the pro-independence Scottish National Party, saying that Mr. Johnson had presided over “nine years of chaotic coalitions already.”

There were laughs from the audience, too, when Mr. Johnson, not known for being scrupulous with his facts, answered a question about personal integrity by saying that the truth mattered.

Near the end of the debate, the conversation landed on a topic that in recent days has overshadowed the election altogether: Prince Andrew’s disastrous interview about his friendship with the disgraced financier Jeffrey Epstein.

Mr. Corbyn said that the monarchy “needs a bit of improvement.”

But Mr. Johnson, who has already antagonized Queen Elizabeth II during his short time in office, said it needed no such thing.

“The institution of the monarchy is beyond reproach,” he said.