When Theresa May says MPs will have the choice between her Brexit deal and crashing out of the EU with no deal, as she did this week in her Panorama interview, she is being neither honest nor democratic. After all, it is parliament, not the prime minister, who is sovereign – and MPs could well decide to ask the people whether they still want to quit the EU.

As the Brexit talks reach their finale, it will be clear that what is on offer isn’t as good as the deal we have got

It’s hard to be sure how the unfolding political crisis over Brexit will play out. But one thing is clear: if MPs want to impose their will on the prime minister, they can, as John Kerr, the former civil servant who helped write article 50, outlines in a new report for the People’s Vote campaign. Although no route to a “people’s vote” is on its own terribly likely, taken together the various scenarios add up to a fairly high chance.

1. MPs amend a motion backing a deal

If May gets a deal, she has to ask MPs to vote for a motion backing it. They could then amend this motion, saying the deal will only go through if the people support it. For this to happen, Labour would have to back a people’s vote. It is edging in the right direction. About 20 Tory MPs would also need to break ranks. So far there are fewer than 10 – including people such as Dominic Grieve and Anna Soubry. But by the time the crunch vote happens, perhaps in the run-up to Christmas, their ranks could swell.

2. MPs reject deal

Another option is for MPs to reject the motion supporting a deal. The prime minister then has to present alternative plans to parliament. If she proposes that we should crash out with no deal, MPs could force her to hold a referendum. For this scenario to play out, MPs first have to reject a deal. That looks quite likely – since Labour is committed to vote against anything like what May is proposing, and hardline Tory Brexiters such as Boris Johnson and Jacob Rees-Mogg are too. But the Mogglodytes probably wouldn’t support a people’s vote. So to get one, a different majority – bringing together the opposition plus pro-European Tory rebels such as Grieve – would probably be needed. That seems quite realistic.

3. MPs amend legislation

Even if MPs vote for the motion backing a deal, they could amend the legislation that would be required to implement it – and demand a new referendum. While it might seem odd for MPs to amend the legislation if they had already backed the motion, some pro-European Tories might prefer to do this as it would look less disloyal to the prime minister. They could also warn, as they voted for the motion, that this was exactly what they were going to do.

‘Theresa May may prefer to get the people to share responsibility for doing anything so crazy.’ Photograph: Sean Gallup/Getty Images

4. May backs people’s vote on her deal

The prime minister herself could decide to put her deal to the people, either because MPs had rejected it or because she feared they would. This might seem a strange thing to do given how adamant May has been that there won’t be a new referendum. But she used to be equally clear that there wouldn’t be a new election – and she called one last year. So she has form when it comes to U-turns. What’s more, it is not clear what better options the prime minister would have in such a situation. She doesn’t want to crash out of the EU without a deal, despite threatening to do so.

5. MPs say no to “no deal”

What if May can’t get a deal? Parliament has already passed legislation ensuring she can’t just let Britain crash out of the EU. If there’s no deal by 21 January, she has to present alternative proposals. MPs could then amend the motion approving those plans, making them subject to a people’s vote. If there is no deal, this is quite a likely scenario. After all, the number of fanatic Tory MPs who are genuinely happy to crash out of the EU may be only about 30.

6. May backs referendum on “no deal”

May could herself ask the people what to do if there’s no deal. After all, she may prefer to get the people to share responsibility for doing anything so crazy.

7. Snap election

Yet another scenario is a snap general election. That doesn’t seem very likely – even if May can’t get MPs to support a deal. Although Rees-Mogg and his gang might vote against a deal, they are unlikely to join Labour in voting down a Tory government. Still, if they were so hopping mad that they did bring down the government, there would probably be an election. Labour might then say it would negotiate a different deal and put it to the people in a referendum. If Jeremy Corbyn did that, he’d probably win the election as pro-Europeans would flock to his banner.

So there are plenty of ways of getting a people’s vote if MPs want one. The snag is that most are still parroting the line that they have to deliver Brexit because that is the “will of the people”. But public opinion is changing – as people see what a pig’s ear the Tories are making of Brexit and realise it is going to be nothing like what Johnson et al promised two years ago.

As the Brexit talks reach their finale, it will be increasingly clear that what is on offer isn’t nearly as good as the deal we have got. At that point, MPs must have the courage to ask the people whether they still want to quit the EU.

• Hugo Dixon is chair of InFacts and one of the founders of the People’s Vote campaign