I have no idea of BALPA's financial position but I would look to the wider union movement. If BA is serious about this, i.e. taking a union to court for following the law to the letter in pursuit of their members' grievances, and it is simply a matter of finances as to which side has greater legal muscle I think you may see the financial involvement of the TUC and the wider union movement, both officially and unofficially. A landmark ruling in BA's favour would be simply too catastrophic in terms of unions' already hobbled freedom of action.
If BA want to take us on, I am a Unison member, then bring it on, this is bullying and posturing and must have been dreamed up by sh1t akin to Deadwood.