My wildfowling club was with WAGBI/BASC from the 1950s, but went over to the Countryside Alliance last year.
BDS would seem the be the one for stalkers, but, locally anyway, they seem to have attracted more than a few poachers/ex-poachers to their ranks.
The St Hubert Club is another club for stalkers.
It all gets a bit political with so many well-paid jobs for people with the gift of the gab and all the people at the top trying to keep their positions/salaries, shooting invites, expenses etc. Could not have said it better myself!