I think it's an issue where whips will be defied by MPs who believe that the national interest is at stake.
If we consider just the Tories, then I wonder how many Tory MPs there are in seats where the locals voted to remain. Probably not many, since, IIRC, it was mostly London where "remain" majorities were returned. OTOH, with a wafer-thin majority, it only needs a few to defy the Government whips.
Labour's position is ambiguous, though. Will we see them whipping MPs to oppose Article 50?
The Unionist parties in NI, I don't know much about. I believe one supported "remain" and the other supported "exit"?
The Lib Dems and the SNP should be solidly against Article 50.
My conclusion? Haven't a clue which way a vote would go. Depends on whether Cons and Labour declare definite positions AND whip their MPs. But also depends on local parties and ordinary people threatening to deselect or vote out MPs who don't vote in accordance with their constituents' referendum wishes.