The next phase of the contest to elect a new Conservative leader has begun amid claims tactical voting to prevent Michael Gove reaching the final two.
Boris Johnson’s team denied such tactics – but at least one of backer suggested some MPs may have switched votes to end Mr Gove’s campaign.
Thursday’s vote put Mr Johnson and Jeremy Hunt top in the race and they will now go head-to-head to become PM.
Mr Hunt promised Mr Johnson “the fight of his life” in the coming weeks.
Mr Johnson’s place in the final two had been widely expected as he had been the frontrunner in all four previous ballots of Conservative MPs, with Environment Secretary Michael Gove and Foreign Secretary Jeremy Hunt vying for second spot.
Two ballots were held on Thursday, resulting in the elimination of Home Secretary Sajid Javid and Mr Gove.
Mr Johnson and Mr Hunt will now have until late July to try to convince the Conservative Party’s 160,000 members to vote for them.
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BBC political correspondent Jonathan Blake said that as soon as the final result was announced on Thursday, MPs began speculating there may have been foul play after analysing the number of votes cast for each candidate.
Five MPs who had supported Mr Javid – Chris Philp, Chris Skidmore, Mims Davies, Kevin Foster and Mike Wood – promised to switch to Mr Johnson in the final ballot.
But Mr Johnson’s vote share increased by just three.
Simon Clarke, who is backing Mr Johnson, suggested some MPs may have “freelanced” outside the official campaign.
“I think some people might have taken it upon themselves to try and steer the outcome, ” he said.
Mr Johnson and Mr Gove previously clashed during the 2016 leadership contest – which saw Theresa May become prime minister – when Mr Gove abandoned Mr Johnson’s previous leadership bid to launch his own.
Some of Mr Gove’s supporters also claimed Mr Johnson’s backers may have voted for Mr Hunt.
However, Mr Gove’s campaign manager Mel Stride dismissed suggestions there had been a vote-switching operation, saying: “It doesn’t seem to me on first observation of this that there has been.
“Because we didn’t see a situation where, as some had speculated, a very large number of votes might have transferred from say Boris Johnson to Jeremy Hunt.
“It would appear to me everybody has behaved pretty much as one would hope they would.”
Sir Alan Duncan, who is supporting Mr Hunt, told Channel 4 News: “There’s talk of one team using proxies designed for their candidate being used for another to boost them.
“Well, you know, this happens in all leadership contests.”
Following the result, Mr Johnson tweeted he was “deeply honoured” to get the backing of 160 MPs – more than half of the total.
Meanwhile, Mr Hunt acknowledged Mr Johnson was the frontrunner to become party leader and prime minister, tweeting that he was the “underdog” but in politics “surprises happen”.
He went on to praise Mr Gove as one of the “brightest stars in the Conservative team” and pledged to “give Boris the fight of his life.”
Mr Gove congratulated his rivals and said he was “naturally disappointed but so proud of the campaign we ran”.
There’s no doubt that Mr Johnson is, at this stage (and there’s a long way to go), widely expected to end up in Number 10.
But this result is an enormous relief to his camp, for the simple reason that they think Mr Hunt is easier to beat.
Forget any differences in style between the two challengers and their comparative talents – Jeremy Hunt voted Remain in the EU referendum.
And for many Tory members it is a priority for the next leader to have been committed to that cause, rather than a recent convert, however zealous.
Mr Johnson and Mr Hunt will now take part in hustings in front of Conservative Party members around the country, before members’ postal votes are counted, with the final result to be announced during the week of 22 July.
They will also take part in a head-to-head debate on ITV on 9 July, following previous leadership debates hosted by Channel 4 and the BBC.
Tory leadership: Tactical voting claims over Johnson and Hunt win}