All eyes are on the Tory leadership contest today as Boris Johnson finally launches his campaign – but behind the scenes, MPs are preparing for an even bigger showdown: the one between the next prime minister and parliament.

Labour has today tabled a cross-party motion that would allow MPs to block no deal, an option several leadership candidates want to keep on the table. It aims to do this by seizing control of the parliamentary agenda on 25 June – an unprecedented move that Nikki da Costa, previously Downing Street’s head of legislative matters, has called “extraordinary”. The plan is a mark of the desperation of MPs who wish to prevent Britain leaving the EU without a deal – it may be their last chance for control over the matter.

How might it work? No deal is currently the default if Britain has not made a deal with the EU by 31 October, and blocking it will involve legislative changes. One plan, drafted by Conservative MP Dominic Grieve, would look to make revoking article 50 the default option instead, but this is seen as a radical move, and is unlikely to secure cross-party backing. Former Conservative minister Oliver Letwin’s solution is said to instead involve changing the standing orders of the Commons. Any legislation introduced is also likely to help stop a prime minister from suspending parliament to force through no deal without the consent of MPs, as threatened by Tory leadership candidate Dominic Raab.

A major hurdle for the motion will be securing the support of Tories, who are wary of appearing to side with Corbyn.

Leadership outsider Rory Stewart appeared to entertain the idea yesterday, saying: “My instinct is I would be wholly supportive of a move that tried to do that”, but his resolve lasted little over an hour, before he tweeted: “For the avoidance of any doubt – I have read the Labour motion proposed for tomorrow and I will NOT be voting for it.”

For the avoidance of any doubt - I have read the Labour motion proposed for tomorrow and I will NOT be voting for it. — Rory Stewart (@RoryStewartUK) June 11, 2019

Even Nicky Morgan, who is strongly against no deal, made it clear she was against the motion. At present the only Tory name on the motion belongs to Letwin, who was key to bids to block no deal in March – but there is also a clutch of Conservative remainers, including Grieve and the former Tory MP Nick Boles, who are said to be considering backing it.

Labour MPs may also hesitate, fearing that the motion would lead to hardline measures such as revoking article 50 or a second referendum, which many have opposed. Some also feel there will be other chances to prevent no deal, without having to resort to an alliance with Conservative rebels. Today’s vote will test whether the party’s recent losses to the Liberal Democrats in the EU elections have softened their stance towards staying in the EU.

Should the vote pass, the prospect of a general election will loom large, and the Tory party may be forced into a choice between an unwanted contest and a gamble over whether parliament would actually vote to revoke article 50 – the only surefire way a no-deal Brexit can be prevented. If it doesn’t, Johnson’s supporters can relax a little: no-deal Brexit lives to fight another day.

• Martha Gill is a Guardian columnist