The Conservative leadership frontrunner will face questions on his Brexit stance in a television grilling for the first time in the campaign on Tuesday, amid frustration among his rivals that he is getting away with pledging to be “all things to all MPs” on issues from Brexit to HS2 in one-on-one meetings with them.

His backers currently include most of parliament’s hardline Eurosceptics, as well as moderates including Matt Hancock, Robert Buckland and Damian Collins, raising questions about how he has won support across the spectrum.

Steve Baker, one of his hardline Eurosceptic backers, set out his belief that “too many leadership candidates think the backstop is the only problem with the withdrawal agreement”, arguing that it would also continue an unacceptable supremacy of EU law over UK law.

The implication was that his preferred choice, Johnson, had told Eurosceptics that he would attempt a more thorough rewriting of the withdrawal agreement as well as meeting his strict deadline of leaving the EU by the end of October. Johnson is said to have told leading Eurosceptics in a private meeting that May’s deal was “dead”.

But at the same time, Johnson has publicly said there would only be a very small chance of a no-deal Brexit under his premiership and has been reinforcing those assurances in meetings with moderate Conservatives.

Dominic Raab’s backers believe their chances of securing Eurosceptic votes have been stunted by his unwillingness to tell them he would entirely rip up the withdrawal agreement – something he has told would-be backers he believes would be impossible to achieve by 31 October.

“Boris has been telling colleagues, of course, ‘I’ll rip up the whole thing,’ yet he’s also securing the votes of centrists like Oliver Dowden,” one MP said. “You could say some of us have been naive not to campaign that way, but also that can really come back to haunt you.”

One rival camp also claimed Johnson had been leaving some MPs with the impression that he was in favour of the HS2 rail project, while others believed that he was against it. Johnson announced in the Birmingham Post on Monday that he would set up a review to “look at the business case for HS2 and to think about whether and how we proceed”.

Johnson has been able to avoid questions about the detail of his Brexit plan as he declined to take part in Channel 4’s debate on Sunday and has only done one newspaper interview since the contest began, plus private hustings for party members and MPs.

At a hustings for journalists in Westminster where Johnson did not turn up, Rory Stewart, one of his rivals, criticised him for seeming to face both ways on Brexit. “Somehow he’s convinced Matt Hancock that he agrees with every word that Matt says, that he’s in favour of the softest of soft Brexits; he’s convinced Robert Buckland that he would never go for a no-deal; and at the same time he’s got Mark Francois roaring: ‘This man looked me in the eyes and promised we’re going out on the hardest of no-deal Brexits,’” Stewart said.

With Johnson absent from the airwaves, his supporters, including Johnny Mercer and James Cleverly, have been dispatched to defend his positions. BBC 5 Live’s Emma Barnett even asked Mercer how many children Johnson had, which he batted away as an intrusion into the frontrunner’s private life.

Johnson is expected to cement his position as the favourite in another round of voting on Tuesday, while Sajid Javid, Stewart and Raab are all battling to get 33 votes from fellow MPs in order to stay in the race.

Each of the three camps suggested they were quietly confident of getting the number if all MPs who had promised to vote for their candidate followed through on their pledge. If all reach that number, the lowest-scoring candidate will drop out.

Jeremy Hunt and Michael Gove are already past that threshold so are likely to stay in the contest, but sources in their camps said they were not expecting a great increase in supporters on the last round.

MPs from all camps said Stewart appeared to have some momentum behind him, as he unveiled David Lidington, Theresa May’s deputy, as his newest high-profile backer, and also gained the support of former chairman Dame Caroline Spelman.

Gove attempted to halt the flow of former remain-supporting Tories to Stewart by writing in the Times that it would be “a mistake to put forward two candidates into the final round who will polarise our party”.

A source in the Stewart campaign said it would be “tight” as to whether he would make the jump from 19 supporters in the first round to 33 in the second, but they believed they had just about enough pledges.

His colourful past also came under scrutiny as he denied in a hustings ever having worked for the MI6 intelligence agency. However, the Telegraph quoted security sources claiming that Stewart had been employed as a spy for about seven years in his 20s.

MPs will vote on their favoured candidates on Tuesday afternoon and then those left in the race will compete in a BBC debate at 8pm – the first television appearance by Johnson since the race kicked off.

All the other candidates have been critical of his low profile in the contest so far, but some have toned down their attacks in recent days as MPs are increasingly seeing his path to victory as unstoppable.

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