I think you misunderstand how Balpa operates. They are a trade union, nothing less nothing more, so they are directed by the membership, in your case, within your company. This is achieved through a 'Company Council', which is comprised of Balpa members voted for by the Balpa members within your company. The CC is usually 3 members + 1 Balpa head office rep. Any agreement must be voted on by the CC, so if you have an agreement not to your liking you have to make that clear to your company reps. Its true Balpa have no stomach for a fight with management (of any company), so it is imperative that your elected CC members stand firm on the needs and desires of all the membership.
Balpa is only the framework, the members MUST be the force for change.