The frontrunner to succeed Theresa May is expected to take questions at his event

Boris Johnson will finally appear in public to launch his campaign to be Tory leader on Wednesday, as one of his rivals cast doubt on whether he could be trusted with access to Britain’s nuclear codes.

Johnson, the frontrunner to succeed Theresa May, will take questions for the first time in the contest at his formal campaign event, where he will saying that “kicking the can” on Brexit would mean “kicking the bucket” for the Conservative party.

The former foreign secretary will want the focus of his launch to be on his Brexit policy, but his character and avoidance of scrutiny in the contest so far came under attack from rival candidates on Tuesday.

Rory Stewart, an outsider in the leadership race, became the first contender to criticise the former foreign secretary personally when he cast doubt on his competence.

Speaking to an audience of 600 members of the public, Stewart said: “Do you really feel that this is the person that you want engaging in the detail of the future of your health and education system? Is this the person you want writing the instruction to the nuclear submarines? Is this the man that you want embodying your nation and guiding you through the most difficult choice we’ve faced for 50 years?”

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He said he “trusted the Conservative members to arrive at the correct answer”.

Two other candidates, Mark Harper and Matt Hancock, also implicitly criticised Johnson’s failure to submit himself to scrutiny in the contest so far, as all of the contenders apart from Johnson and Jeremy Hunt confirmed that they were happy to take part in television debates.

Harper, who has about six public backers among MPs, said all candidates must be open to public questioning and scrutiny, and that any other route would risk a similar situation to the 2017 general election, when Theresa May’s campaign style stumbled.

“If you want to lead this country, you have to be prepared to set out your stall,” he said. “I think you have to open yourself up to questioning and be prepared to level with people and be questioned about it. We had a general election campaign two years ago and the prime minister demonstrated she was not as good at campaigning as we all thought she would be.”

Hancock said: “I certainly think that everybody who puts their name forward to be prime minister should be open to scrutiny, should be accountable. Everybody should participate in the proposed TV debates. And I think we’ve got to ask the question, why not? I’ve got nothing to hide and that’s why I am here.”

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David Lammy, a Labour MP who supports the People’s Vote campaign for a second referendum, criticised Johnson for wanting to “force a destructive no deal on our country, when he doesn’t have the guts to face the people”.

A source on Johnson’s campaign said the frontrunner would take questions from the media at his launch and was still considering bids from BBC and other broadcasters for him to take part in live hustings.

Johnson is expected to be asked about his admission of having tried cocaine in the past, after his fellow contender, Michael Gove, became mired in a controversy about his previous use of the class A drug.

He is also likely to be questioned about how he can square his promise to hardline Brexit supporters that he is prepared to ditch May’s withdrawal agreement and leave with no deal if necessary on 31 October with his suggestions to soft Brexiters that he would try to avoid leaving without a deal.

Johnson is expected to say in his speech: “Now is the time to unite this country and unite this society, and we cannot begin that task until we have delivered on the primary request of the people, the one big thing they have asked us to do: after three years and two missed deadlines, we must leave the EU on 31 October.

“We simply will not get a result if we give the slightest hint that we want to go on kicking the can down the road with yet more delay. Delay means defeat. Delay means Corbyn. Kick the can and we kick the bucket.”

He will also attack the Labour leader directly, saying he was capable of beating a leftwing candidate when he defeated Ken Livingstone twice to become mayor of London.

“We cannot let them anywhere near Downing Street and I would remind you that the last time I faced an emanation of that Marxist cabal I defeated him when the Conservatives were 17 points behind in London. And we can do it again,” he will say.

Sajid Javid, another leadership contender, is also planning to launch his campaign on Wednesday, calling for change at the top of the Conservatives.

“I believe now more than ever that this is a moment for a new kind of leadership and a new kind of leader,” he will say. “A leader is not just for Christmas, or just for Brexit. So we can’t risk going with someone who feels like the short-term, comfort zone choice. We need tomorrow’s leader, today.”

Javid released a leadership video on Tuesday highlighting his background as the son of a bus driver who arrived in the UK from Pakistan in 1961 with £1 in his pocket.

“There was too much chance in my story, and too many kids I grew up with weren’t so lucky. For me hard work, public services, and my family were how I got ahead in life,” he will say at his launch.

“So I want to learn from that and level the playing field for the next generation. I want everyone in this country to feel that if they have a go, they will have the opportunity to succeed.”