BOURNEMOUTH, England — His shirt sleeves rolled up, Britain’s foreign secretary, Jeremy Hunt, bounded into the hall, ignored the lectern and headed straight to the front of the stage to make his pitch that he should lead the country out of its paralyzing Brexit maze.

But right from the start, Mr. Hunt was playing catch-up. He is one of two candidates to be Britain’s next prime minister, and his rival and predecessor as foreign secretary, Boris Johnson, had already won cheers from this audience with his crowd-pleasing, pro-Brexit bombast. And, earlier, Mr. Johnson had grabbed eye-catching headlines by claiming that he would beat Mr. Hunt in a naked mud-wrestling contest.

Tall, lean and fit, the serious-minded Mr. Hunt would probably more than hold his own against his less-toned opponent, but defeating the theatrical Mr. Johnson for the Conservative leadership is another matter.

The two men are competing for the votes of about 160,000 Conservative Party members, who will choose a new leader, and prime minister, next month, as the Conservatives hold a working majority in Parliament. They faced off directly on Tuesday night, in a televised debate that the foreign secretary had pressed for to make his case.