The Tory leadership hopeful Matt Hancock has laid into his rival Boris Johnson for dismissing business warnings against a hard Brexit, saying: “To the people who say fuck business, I say fuck fuck business.”

Hancock also poured cold water on the claims of candidates who said they would take the UK out of the EU by the end of October whether or not there was a deal.

“The brutal reality is, ‘no deal’ is not a policy choice available to the next prime minister,” he said.

Johnson was reported last year to have said “fuck business” when questioned about the sector’s concerns over a no-deal Brexit, although sources close to him say he was referring to anti-EU business lobby groups rather than companies.

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His remarks outraged many Conservatives, however, and the digital minister, Margot James, recently said they made him unfit to hold high office.

Hancock, the health secretary, has set out his pitch alongside Jeremy Hunt that a no-deal Brexit would be all but impossible given parliament’s opposition to that outcome. Hunt said this week that pursuing a no-deal policy would be “political suicide” because it would lead to a general election.

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With acrimony growing between some of the candidates over their Brexit stances, Dominic Raab published a “clean campaign” pledge under which hopefuls promise not to attack each other personally. It was signed by Sajid Javid and Hancock but the move quickly turned into a row when the Eurosceptic Steve Baker pointed out that it had been published before the other candidates had been asked to put their names to it.

“Schoolboy dirty tricks like this could kill the Conservative party. It is imperative this campaign is genuinely clean,” Baker said.

John Bercow, the Commons Speaker, fired a warning shot at the candidates open to no deal on Tuesday by saying he planned to stay on in the chair while Brexit was still unresolved and signalled he would not allow parliament to be sidelined.

Johnson has been joined by Raab and Esther McVey in arguing that the UK must leave on 31 October with or without a deal. McVey set out her hardline stance in the Telegraph, where she wrote: “We need to stop wasting time having artificial debates about renegotiating backstops or resurrecting botched deals.”

An 11th candidate, James Cleverly, announced his candidacy to his local paper on Wednesday, saying the Conservatives needed to “look new and sound different”. More are expected to declare in the coming days, but Johnson remains the frontrunner.

Hunt was thought to be the leading candidate among MPs, but some of the rival camps believe he is losing ground to Michael Gove, the pro-Brexit environment secretary.

The development secretary, Rory Stewart is an outlier in the contest. He is against a no-deal Brexit and is touring Britain talking to the public. He will be in the leave-voting area of Wigan on Wednesday.