If BALPA can sell British pilots to British airlines to fill low-hours positions, then they will be helping. At the moment there is an inordinate number of French and Dutch pilots filling low-hours positions with British airlines.
It is the right of all EU nationals to be able to work in any EU nation. BALPA has no influence over this, a fundamental tenet of the EU. If you wish to register your desire for the UK to leave the EU, there are several political parties who espouse this point of view. BALPA must work within the EU's legal framework, and it is not mandated to lobby for the UK's exit or exemption from EU employment legislation.
Edit: I've just had to delete a xenophobic rant by one Ppruner. I will not tolerate any such posts on this forum, so don't push it!
Scroggs