LONDON — Accused of hiding from scrutiny, the front-runner to become Britain’s next prime minister, Boris Johnson, the former foreign secretary, on Wednesday finally took questions from reporters — and then dodged queries about Brexit and whether he had used cocaine as a college student.
Speaking in central London, Mr. Johnson said that it was essential that Britain leave the European Union by the current deadline of Oct. 31 and that he expected to do so with a deal, though the possibility of a no-deal exit needed to be retained as negotiating leverage.
Mr. Johnson, who campaigned for Brexit in the 2016 referendum, emphasized that he was “not aiming for a no-deal outcome.” But he said that the possibility of a no-deal exit was a “vital tool of negotiation” and that Britain “must do better than the current withdrawal agreement.”
“Delay means defeat,” he said at an event to start his Conservative leadership campaign, adding that for a Conservative-led government to kick the Brexit can down the road means “we kick the bucket.”
He declined, however, either to say whether he would resign if, as prime minister, that Oct. 31 deadline was not met, or to explain how a better deal would be extracted from the European Union. Most analysts believe that a no-deal Brexit would be economically damaging and potentially chaotic, and on Wednesday opposition lawmakers were planning to try to start a process that they say could make it impossible for Britain to leave the bloc without an agreement.
On Wednesday, the Financial Times cited a leaked cabinet note stating that it would take “six to eight months” to build up supplies of medicines for a no-deal Brexit and “at least 4-5 months” to improve trade readiness for the new border checks that might be required.
After Mr. Johnson’s set-piece speech, he took a few questions — with a limit of six — mostly about his character. He is one of the country’s best-known political figures but now a polarizing one, thanks to his 2016 Brexit campaign and subsequent remarks — many of them in his weekly column in the Daily Telegraph, which pays him 275,000 pounds a year, or about $350,000.
His most striking evasion on Wednesday was over the question of cocaine use, an issue that has already wrecked the leadership campaign of Michael Gove, the former environment secretary, who acknowledged that he had taken the drug two decades ago, an admission that opened him up to accusations of hypocrisy.
On a television show Mr. Johnson had once previously made light of the issue, suggesting he sneezed when offered a white powder. But asked on Wednesday whether his more detailed description of taking cocaine, given in GQ magazine some years ago, was true, Mr. Johnson dodged the question, saying merely that the “canonical account” of the incident had already been given, perhaps a reference to his televised comments, before changing the subject.
Mr. Johnson is the odds-on favorite to succeed Theresa May as leader of Britain’s Conservative Party, a position that brings with it the job of prime minister, providing the successful candidate can retain the current narrow working majority in Parliament.
The first stage of the process begins on Thursday, when Conservative Party lawmakers start balloting to draw up a shortlist of two candidates, one of whom will eventually be chosen in voting by around 150,000 members of the party.
Rivals say that Mr. Johnson has consolidated his leading position by keeping a low profile and minimizing the risk of making any mistakes that could set his campaign back, mindful perhaps of the self-inflicted harm he has caused through numerous verbal gaffes.
The contest takes place at a time of crisis in British politics after the country’s failure to leave the European Union on schedule on March 29.
Facing a challenge from Nigel Farage’s Brexit Party, many Conservative Party lawmakers seem ready to overlook Mr. Johnson’s past indiscretions and colorful private life in the hope that he can deliver Brexit and then win a future general election.
But rivals for the leadership have attacked Mr. Johnson’s refusal to give any broadcast interviews where he could be interrogated in detail, suggesting a weakness that would make him vulnerable as prime minister.
Mr. Gove seemed to be targeting Mr. Johnson, without naming him, by complaining about a candidate hiding “in his bunker.”
The health secretary, Matthew Hancock, argued that all those seeking the job “should be open to scrutiny” and give broadcast interviews, and Mark Harper, a former chief whip and another contender in the crowded leadership race called on Mr. Johnson to give “clear answers” about his cocaine use.
Mr. Johnson’s appearance at the news conference was seemingly arranged to answer some of the criticisms, yet access to the event was strictly controlled, and some reporters were turned away.