Hi Broomstick,
I dont know about BALPA, but IPMS (just changed their name to PRospect for some reason too complictaed to worry about), represent us at our unit. They have reduced rates for people in your situation, as I'm sure that other unions do.
The only problem with being in your shoes, (correct me if I'm wrong), is that to be effective the union has to be recognised by the employer. Although their is now a legal requirement for employers over a certain staff number to recognise a union, it only has to be the one that the majority of staff belong to. I know that IPMS/Prospect and the TGWU have their own specialist aviation departments.
It won't hurt for you to approach BALPA/TGWU or IPMS, they should tell you straight away if they can't help you.