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https://www.theguardian.com/politics/2018/may/29/labour-mps-fear-brexit-voters-unfounded-study
Handful of constituencies.
As for poaching conservative seats, they gained votes last due as people tactical voted to keeps the cons out. They may lose those votes this time.
Problem is of course, as you say, that there is no guarantee either a good remain / very light brexit vision gains votes esp. not with the current scandal discussed here.
But I dont see this work either. But the party may evolve it's stance again.
Though they did put ending freedom of movement on their plans. That means no single market but perhaps they will change that stance.
On what basis? A lot of ex-industrial towns which were labour strongholds voted for Brexit and a lot of them haven't changed their mind about it.
Labour coming out and opposing Brexit would trash their chances of winning in a lot of constituencies (and not just in the immediate future but further down the line as well, the lib dems show that the electorate have a long memory) and, with Corbyn in charge, it's unlikely that they're going to poach enough conservative seats to make up for that.
Blair might have been able to manage that tactic but I can't see it working at the moment.