Birmingham airport security fast track

Hopefully I'm not being pedantic, but you're getting your terminology mixed up and it might prevent you from finding what you're looking for.

You don't go through security when you arrive into the UK on the return journey, you only go through passport control and customs. Passport control is where the potential delays are. That will be why you're only seeing fast track security for the journey out, as that's the only place where it's applicable.

Fast track for passport control MIGHT be available, but it's generally given out by the airlines for their passengers with more expensive tickets.