Maybe someone who understands the mechanism of Parliament will know:
Can an MP propose a bill to have a referendum, and then cross party MPs vote it through? Is this viable? So even if May and Corbyn are prevaricating it could be forced through?
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The only way to have a non-Government bill is a Private Member's Bill. So the scenario you describe would need a People's Vote adherent to get lucky in the ballot, and anyway those bills are very vulnerable to filibustering. Generally they only succeed if uncontroversial.
[Edit: In fact, there is
just such a bill lurking, introduced by Gareth Thomas. It gets its second reading late in October, but it won't get anywhere]
Fortunately, we don't need a bill for a referendum. It could simply be raised - in either House - as an amendment to a tangentially-related bill. Brexiteers and Remainers on both sides have done quite a lot of that. It's not clear whether the "meaningful vote" will be amendable, but there's bound to be some legislation before March that could be used as a vehicle. The Speaker decides which amendments to select, making a judgement on which are most likely to pass, and luckily Bercow's on the side of the angels.
However, the maths are terrible for a bill that isn't supported by either May or Corbyn.
Personally, I think that if the alternative is no deal, and all opposition parties whipped in favour of a plebiscite, the Conservative rebels would greatly outnumber the Labour leavers. And, of course, a second vote is now Labour policy, if only in certain circumstances.
The difficult question is whether Corbyn and his cabal would whip in favour of a referendum with an option to remain, and if any referendum mechanism would get agreement from LDs, SNP, Labour and Soubryites.