Boris Johnson has been accused of giving MPs contradictory promises on Brexit to win their votes, as one of his highly Eurosceptic backers warned that hardliners want to see him effectively tear up Theresa May’s deal with the EU.

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.

Q&A What does a no-deal or WTO-rules Brexit mean? Show Hide If the UK leaves the EU without a deal it would by default, become a “third country”, with no overarching post-Brexit plan in place and no transition period. The UK would no longer be paying into the EU budget, nor would it hand over the £39bn divorce payment. The UK would drop out of countless arrangements, pacts and treaties, covering everything from tariffs to the movement of people, foodstuffs, other goods and data, to numerous specific deals on things such as aviation, and policing and security. Without an overall withdrawal agreement each element would need to be agreed. In the immediate aftermath, without a deal the UK would trade with the EU on the default terms of the World Trade Organization (WTO), including tariffs on agricultural goods. The UK government has already indicated that it will set low or no tariffs on goods coming into the country. This would lower the price of imports – making it harder for British manufacturers to compete with foreign goods. If the UK sets the tariffs to zero on goods coming in from the EU, under WTO “most favoured nation” rules it must also offer the same zero tariffs to other countries.

WTO rules only cover goods – they do not apply to financial services, a significant part of the UK’s economy. Trading under WTO rules will also require border checks, which could cause delays at ports, and a severe challenge to the peace process in Ireland without alternative arrangements in place to avoid a hard border.

Some no-deal supporters have claimed that the UK can use article XXIV of the General Agreement on Tariffs and Trade (Gatt) to force the EU to accept a period of up to 10 years where there are no tariffs while a free trade agreement is negotiated. However, the UK cannot invoke article XXIV unilaterally – the EU would have to agree to it. In previous cases where the article has been used, the two sides had a deal in place, and it has never been used to replicate something of the scale and complexity of the EU and the UK’s trading relationship. The director general of the WTO, Roberto Azevêdo, has told Prospect magazine that “in simple factual terms in this scenario, you could expect to see the application of tariffs between the UK and EU where currently there are none”. Until some agreements are in place, a no-deal scenario will place extra overheads on UK businesses – eg the current government advice is that all drivers, including lorries and commercial vehicles, will require extra documentation to be able to drive in Europeif there is no deal. Those arguing for a “managed” no deal envisage that a range of smaller, sector-by-sector, bilateral agreements could be quickly put into place as mutual self-interest between the UK and EU to avoid introducing or to rapidly remove this kind of bureaucracy. Martin Belam

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.

Play Video 2:01 Tory leadership candidates take aim at no-show Boris Johnson in TV debate - video

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.

Quick guide Tory party leadership contest Show Hide What happens next in the Tory party leadership race? As she announced on 24 May, Theresa May stepped down formally as Conservative leader on Friday 7 June, although she remains in place as prime minister until her successor is chosen. In a Conservative leadership contest MPs hold a series of votes, in order to narrow down the initially crowded field to two leadership hopefuls, who go to a postal ballot of members.

How does the voting work? MPs choose one candidate, in a secret ballot held in a committee room in the House of Commons. The votes are tallied and the results announced on the same day. In the first round any candidate who won the support of less than 17 MPs was eliminated. In the second round anybody reaching less than 33 votes was eliminated. In subsequent rounds the bottom placed contender drops out until there are only two left. The party membership then chooses between them. When will the results be announced?

The postal ballot of members has begun, and the Tory party says it will announce the new prime minister on 23 July.. Photograph: Neil Hall/EPA

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.

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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.