LONDON — Prime Minister Boris Johnson and his challenger, Labour leader Jeremy Corbyn, staged their first debate of the election campaign on Tuesday night — and what was most notable were the sharp, aggressive questions from the audience, which expressed open mistrust, even disgust, for both candidates.

The debate on ITV showcased a dozen ordinary voters allowed to ask their questions.

First up: “Both of you say Brexit will be resolved in the next few months. But there have been so many broken promises. Can you assure me we won’t be talking about it forever?”

Johnson promised he had a Brexit deal ready to pop into the oven, heat and serve.

Corbyn said it was “nonsense” to say Johnson could complete Brexit by January. He said a trade deal with the European Union would take seven years to negotiate.

Later in the one-hour debate, another voter asked: “How can we trust you?”

The question got a round of applause. The questioner continued: “The debate has become toxic, with an appalling level of lies. How can we trust you to bring this country together?”

Johnson answered that the problem was that Parliament has blocked Brexit. The way to restore trust is to get Brexit done, he said.

Moderator Julie Etchingham asked, “Does the truth matter in this election?”

Johnson replied, “I think it does.”

The audience laughed.

During the debate, the Conservative Party rebranded its Twitter account to read “FactCheckUK” and then proceeded to tweet messages such as: “@BorisJohnson is the clear winner in tonight’s LeadersDebate.”

Full Fact, an actual fact-checking outlet, tweeted that the Conservative Party messages were “inappropriate and misleading” and advised its followers against mistaking the source “for an independent fact checking service.”

Etchingham pressed Johnson on his broken pledge to have delivered Brexit by Halloween. “You promised 40 times that we would be out of the E.U. on October 31,” she said. “One of your staff once said you had betrayed everyone who worked with you.”

She then turned to Corbyn, asking him: “Can you take responsibility for anti-Semitism in your party?”

The Labour Party has been dogged for years by accusations of anti-Semitism, and a BBC documentary that aired over the summer accused the party’s leadership of undermining efforts to address it.

Corbyn called anti-Semitism a “scourge” and said his party had worked hard to root it out.

Johnson said he would get Brexit done — and challenged Corbyn again on his position on Britain’s leaving the European Union. Corbyn said he would quickly negotiate a new, softer Brexit deal with the E.U. and then take it to the public in a second referendum.

The moderator asked, “Will you promise to improve the nature of debate if you become prime minister?’

After a bit of goading, the two awkwardly shook hands.

Toward the end of the debate, the two candidates were peppered with rapid-fire questions with a request for short answers.

“Leaving politics aside,” Etchingham asked, what would they get each other for Christmas?

Corbyn said he would give Johnson a copy of the Charles Dickens classic “A Christmas Carol,” so he could reflect on the character Scrooge.

Johnson said he would give Corbyn a copy of his Brexit deal.

Both leaders were asked whether the monarchy was “fit for purpose,” a Britishism for something well-suited for its designated role.

Corbyn, who in the past has expressed republican beliefs, said the monarchy needs “a bit of” improvement, triggering laughter from the audience.

Johnson said “the institution of the monarchy” was “beyond reproach,” prompting Twitter users to post his comments alongside pictures of Prince Andrew, the queen’s second son, who has dominated headlines after a disastrous BBC interview in which he defended his friendship with the late convicted sex offender Jeffrey Epstein and was roundly panned for not expressing concern for the women who said Epstein had victimized them.

Asked about Andrew specifically, Johnson and Corbyn avoided comment. Corbyn said the focus — and Johnson agreed — should be on the victims of Epstein, the disgraced financier who committed suicide in New York in August while awaiting trial on federal charges of sex trafficking.

Corbyn is trailing overall in a sample of recent opinion surveys and, given that he did not break through during the debate, will hope to generate more excitement Thursday with the launch of his party’s election manifesto.

Three more one-on-one debates are scheduled, as well as encounters involving second-tier parties. The Liberal Democrats and the Scottish National Party lost a court bid for their leaders to be included in the debates with Johnson and Corbyn.