Dominic Raab, the former Brexit secretary who positioned himself as the hardest Eurosceptic candidate, was dumped out of the Tory leadership race on Tuesday, as his camp blamed Brexiters for flocking en masse to Boris Johnson.

Raab had assembled an impressive team of former Vote Leave operatives to run his campaign but failed to gain the 33 votes needed from his party colleagues to progress to the third stage of the vote on Wednesday.

The home secretary, Sajid Javid, scraped past Raab to just meet the 33-vote threshold, but both were leapfrogged by Rory Stewart, who has run an insurgent campaign on social media.

Even minutes before the vote, teams backing Raab, Javid and Stewart all seemed uncertain they would progress. Stewart said he was “delighted” at the result but added: “There’s a long way to go. I’m still very much the underdog in this race.”

Tory leadership: Johnson, Hunt, Gove, Stewart, Javid through, as Raab eliminated – live news Read more

MPs cited three issues for Raab. They blamed a failure to win over a solid bloc of votes from the hard Brexit European Research Group, who have backed Johnson, as well as a “Stop Raab” operation by moderate Tories who saw him as the most extreme candidate and his refusal to rule out proroguing parliament, which rival candidates openly attacked him for.

Raab had recruited Vote Leave’s head of communications, Paul Stephenson, to run his campaign as well as other former senior staff from the leave campaign team and won earlier endorsements from former cabinet ministers Maria Miller and David Davis, as well as the children’s minister, Nadhim Zahawi, who had backed Johnson in 2016.

Sources in the Raab campaign said they believed he had lost out on ERG votes because he had not been prepared to say he would tear up the EU withdrawal agreement in its entirety – which they said Johnson had promised supporters he would do.

“It just wasn’t realistic, but perhaps we were naive about what other campaigns would promise,” one Raab-backing MP said.

His team had been making the case over the past 24 hours that there should be two Brexiters who believed in no deal put through to the next round, because of the risk of Johnson imploding.

However, he failed to win the endorsements from either of the Eurosceptics knocked out of the race, Andrea Leadsom and Esther McVey, who both backed Johnson.

Mark Francois, the strongly pro-Brexit MP who supports Johnson, said Raab’s elimination was sad. “Whoever wins, and I hope it’s Boris, I hope they find a good place for Dom in their cabinet, because I think he deserves it.”

Javid was the first of the leadership candidates to offer an olive branch to his defeated rival. In a tweet, he praised his “professionalism, drive & fresh ideas” and said Raab had “a major role to play with any new PM helping Britain’s young people get a fair shot”.

Raab’s backers are more likely to go to Johnson, though some are thought to be more inclined to back Michael Gove, meaning the environment secretary has a chance of overtaking Jeremy Hunt.

Javid’s backers insisted he was staying the race until the next ballot and sources around both Javid and Stewart pointed to the stalling momentum of Hunt, Gove and even Johnson, who put on just 12 votes despite also winning the endorsement of the former leadership candidate Matt Hancock.

MP Simon Hoare, one of Javid’s key backers, said there was still time for the home secretary to pick up momentum in the next 24 hours, at the expense of Hunt and Gove.

“There is still time for us to speak to colleagues about how we frame the next stage of this contest,” Hoare said. “There will be some disappointment in Boris’s team tonight because it’s a lower than they thought they’d gain. But he is clearly in the final two.

“And so the other candidate must be someone for whom life-changing, meritocratic Conservative values is not gleaned from a dusty textbook, it’s life experience.”

Sources around Javid’s campaign said the 10-vote gain he made on the previous round had been more than they expected at the beginning of the day and aides hurried to prepare the home secretary for the BBC debate shortly after the result, one they had not been certain he would be able to participate in.

Hunt remained in second place but Stewart’s backers said they believed they could win over supporters from the foreign secretary as his momentum stalled. He added just three votes to his first-round total.

Gillian Keegan, the Chichester MP and supporter of Stewart, said the momentum was with the international development secretary. “They’re very close now. There’s a clear winner, and between the others there’s not many votes,” she said.

“It’s very rewarding. Rory’s campaign is basically honest about where we are as a country. He’s basically telling people the uncomfortable truth in some cases, but he’s being honest. And who knew there was a market for honesty in politics? I’d always hoped that there was.”

MPs will vote again on Wednesday, and if necessary on Thursday, until the field is narrowed down to just two names, which will then be offered to Conservative members in a postal ballot. The result will be announced in the week beginning 22 July.