A campaign to stop Boris Johnson becoming prime minister and taking the country into a no-deal Brexit was launched by moderate cabinet ministers on Saturday as the first shots were fired in the Tory contest to succeed Theresa May in Downing Street.

After May bowed to pressure on Friday and announced she would resign as Tory leader within two weeks, justice secretary David Gauke and international development secretary Rory Stewart condemned Johnson’s readiness to embrace a no-deal, saying it would be hugely damaging to the national interest.

The move, part of a concerted “anti-Johnson” push by opponents of a hard Brexit, followed comments by the former foreign secretary on Friday, soon after May’s resignation speech in Downing Street, that the UK would definitely leave the EU “deal or no deal” on 31 October if he became leader in July.

The remark infuriated the soft-Brexit wing of the party, with some MPs and ministers even warning that there would be “serious numbers” of moderate Conservatives who would be ready to vote down a Johnson government if he set the country on a path to no deal.

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In a clear attack on Johnson, Gauke, writing in today’s Observer, warns that candidates who fail to acknowledge the “enormously harmful” effects of crashing out of the EU will fuel populism and risk doing untold harm to the economy and national interest.

“All those that do have such aspirations have a responsibility to set out their approach to Brexit, which is anchored in the hard realities of the situation. We should not pretend that leaving the European Union without a deal will be anything other than enormously harmful to our economy, weaken our security relationships and threaten the integrity of the union,” said Gauke.

His comments come ahead of the release of European election results, which are expected to show Nigel Farage’s Brexit party trouncing the Conservatives.

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“There is too often reluctance in pointing out the likely outcome of no deal. The pretence by people who should know better that no deal is somehow manageable – or could be addressed simply by ‘proper preparation’ – has only encouraged a growing part of the population to be unwilling to make any kind of accommodation with the EU. Loose talk about no deal has helped give credibility to the simplistic slogans of the Brexit party.”

The warnings by Gauke – expected to be endorsed by the chancellor, Philip Hammond, in media interviews – came after Stewart, who has declared his intention to stand, tore into Johnson and said he would refuse to serve in a government under his leadership.

Stewart said: “I spoke to Boris, I suppose, about two weeks ago and I thought at the time he had assured me that he wouldn’t push for a no-deal Brexit. So, we had a conversation about 20, 25 minutes and I left the room reassured by him that he wouldn’t do this.

“But it now seems that he is coming out for a no-deal Brexit. I think it would be a huge mistake. Damaging, unnecessary, and I think also dishonest.”

Facebook Twitter Pinterest Rory Stewart has declared his intention to stand in the Tory leadership contest. Photograph: Mark Thomas/Shutterstock

The warnings came as senior moderate Tories grew increasingly alarmed at signs that Johnson is already winning over MPs who fear that, if they do not back him, a more hardline candidate will emerge as the champion of pro-Brexit Tories in parliament and in the country.

One senior Tory source said Johnson held appeal because he was seen by fellow MPs and Tory members as a winner after Theresa May, whose disastrous 2017 election campaign rid the party of its majority. “The unpalatable truth about the situation is that whether we like it or not, in terms of marginal seat polling, Boris is still outperforming everyone else.”

On Saturday the list of candidates entering the race grew as health secretary Matt Hancock threw his hat into the ring, saying he believed May had not been clear enough about the trade-offs required in reaching a Brexit deal.

“She didn’t start by levelling with people,” Hancock said. “I think it is much, much easier to bring people together behind a proposal if you are straightforward in advance.”

Former Brexit secretary Dominic Raab also formally entered the race with a call for a “new direction”.

The MP for Esher and Walton, who resigned over May’s withdrawal agreement, told the Mail on Sunday: “The country now feels stuck in the mud, humiliated by Brussels and incapable of finding a way forward. The prime minister has announced her resignation. It’s time for a new direction.”

Foreign secretary Jeremy Hunt and ex-Commons leader Andrea Leadsom are the latest heavyweights to have also announced bids for the Tory crown.

Writing on theguardian.com, former cabinet minister Justine Greening said the Conservative party now faced “electoral oblivion” as a new leader would “test its hard Brexit theory to destruction”. Greening, who backs a second referendum, said that the party was engaged in “a debate with itself about what type of electoral cyanide to take”.

Dominic Grieve, the former attorney general, said: “Whoever gets the leadership of the party, a new leader in itself does not solve the crisis we are facing. It does not appear likely that there is a majority in parliament for any deal and there is clearly a majority against a no-deal Brexit. That suggests the only two options available are a general election or a referendum to resolve the matter.”