Peterborough voted 61% Leave yet returned a Labour MP.Do you not think a Labour leaver betrayed by his party would not be tempted to switch and still be as loyal? I would say many with a strong leave/remain view hold a single issue position that transcends loyalties and would be likely to lend their vote as a one off to another party in a GE. Switching from Labour to Tory might be a stretch, but to the BXP perhaps less so...
Let's see with a specific example of a constituency then from before the BXP was even formed.
Dudley. Labour WIN in 2017 by 22 votes. Voted by almost 70% to leave the EU in the referendum.
If Labour come out for a second referendum/remain and the BXP fight that seat at the next GE who wins there now? The leave vote is split and Labour hold? What about if the BXP/Tories formed a pact as a result of the new Labour policy, that changes things no?
There are dozens of marginal seats in the exact same position with an unpredictable outcome and everything for the BXP to fight for if Boris fails to deliver his Oct 31st do or die promise. The Tories and Labour are in the unenviable position of having everything to lose, for the BXP everything is up for grabs.