Fabio/Ranger, you may want to read the Trade Union Labour Relations Consolidation Act 1992, which does not include strike action as a precursor for removal of benefits that are not contractual. It gives employees the protection “not to be subjected to any detriment” by an employer’s action, or lack of action, taken “for the sole or main purpose of preventing or deterring him taking part in the activities of an independent trade union at an appropriate time or penalising him for doing so. However strike action itself is not covered, so BA removing a discretionairy benefit of Staff Travel is not covered by the act and is also not a contractual obligation by BA. They had every right to remove it, especially as you were warned that they would.
So you may want to ask your rep what they base their demand for reinstating ST on, it is not the law, so not sure what they do base it on.
You may not like it, and I can understand that, but that is not grounds for taking legal action. Liking or not liking is irrelevant, you need the law to support you or have precedent and in your case for reinstating ST, you have neither.