On the basis of a complete lack of legal training, my understanding is that a strike is generally illegal only in the sense that it is a breach of contract and contrary to civil law. Except in very special cases, such as in the Police, striking is not a criminal offence.
The portions of the relevant laws that have been quoted on this and the Airline Employeed Only thread mention only protection against unlawful dismissal for taking part in a lawfully constituted strike. I have seen no mention of protection from any other sanctions that an employer may take against strikers.
I suspect that even though the first two strikes were not properly called, and so strikers continued employment was formally not protected, any one dismissed because they struck would have a reasonable chance at a tribunal to claim that they acted in good faith, based on information they were entitled to believe that the strike was properly established. They could well have a case against BASSA for recovery of any costs they incurred through striking. Perhaps they could force BASSA to pay the difference between ST fares and public fares for any flights they, and their families and friends, take on BA - forever!