Matt Hancock, the latest candidate to drop out of the contest to succeed Theresa May as prime minister, could end up endorsing Boris Johnson, the frontrunner, despite having pitched his own candidacy around a softer Brexit and a change from traditional Conservative politics.

Hancock, the health secretary, was the youngest of the seven contenders remaining after Thursday’s first round, but announced on Friday he was withdrawing after coming sixth out of the seven.

“I ran as the candidate of the future, but the party is understandably looking for a candidate for the unique circumstances we face right now,” he said in a statement, not saying who he might back next.

Hancock will spend the weekend weighing up the merits of Johnson and Michael Gove, having declined an offer from Sajid Javid to form an alliance of “change candidates”.

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Hancock was said to have feared that with Javid’s support only just ahead of his own – the home secretary got 23 votes – he would be backing a candidate who might struggle to make it beyond Tuesday’s second round.

Hancock held a meeting with Javid on Thursday, but sources in the health secretary’s campaign said the discussion had not been fruitful. Gove’s team had also been making overtures to Hancock, believing their candidate could take on Johnson most effectively.

The Johnson ally Gavin Williamson opened channels of communication with the Hancock camp on Thursday, as it became clear he had little hope of progressing further, the Guardian understands.

Unlike Rory Stewart, Hancock has been careful not to criticise Johnson during the campaign – apart from repudiating reported anti-business comments. Hancock is a former adviser and longtime ally of George Osborne, whose Evening Standard editorial on Thursday appeared to be edging closer to supporting Johnson.

Facebook Twitter Pinterest Matt Hancock leaves parliament on Friday. Photograph: Alastair Grant/AP

The same newspaper ran an editorial on Friday praising Hancock as “part of the Conservative future” and a candidate who had “laid out the home truths facing the new prime minister on Brexit”.

While he has staked his bid for No 10 on delivering Brexit by 31 October, Johnson has also stressed his pro-business credentials, and said in an interview on Friday he would pursue “modern, progressive Conservatism” in office – similar language to that used by Hancock in his own campaign pitch.

The next steps for Hancock, as well as Javid, are unclear. One Hancock supporter said a “dream ticket” somehow combining Gove, Javid and Hancock, could still emerge.

Javid remains an outsider, and could struggle to reach the 33-vote tally needed to reach the next round. A supporter of the home secretary said part of his pitch would be to accept that Johnson would inevitably win and seek to persuade Conservative MPs to put him in the final two to be voted on by party members as a way of illustrating the Tories’ new image.

“Even if you think Boris is a shoo-in, then you need to think about who’s best placed to test him,” they said. “You also might want to think: who else do we want on TV for four to six weeks, representing the party? How about someone who makes it look good, and look different?”

There is also the issue of whom Hancock’s supporters might now back. One said: “I don’t think there will be a unified view – some to Michael Gove, or Boris Johnson or Jeremy Hunt.”

May’s former de facto deputy Damian Green is among Hancock’s public backers. On Friday he tweeted: “I am proud to have supported Matt Hancock and the values he stands for. He will be a great PM one day. Meanwhile, to all candidates, until Monday, Do Not Disturb.”

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Hancock’s pitch to his colleagues had been that he was best-placed to appeal to voters in the centre ground of British politics, but that meant appealing to a similar group of MPs to Stewart. The international development secretary received 19 votes but has said he is determined to continue with his quixotic #RoryWalks campaign, insisting he is the best person to take on his fellow old Etonian Johnson.

Hancock told the Guardian on Wednesday: “Of course we’ve got to deliver Brexit; but then we’ve got to win a majority by appealing to aspirational people in the centre ground of British politics, where there’s a gaping hole.”

He added: “There are some candidates who won’t be able to bring the Conservative party with them, and there are others who will find it more difficult to reach into the centre ground. I think I’m best placed to be able to do both.”