I find it hard to believe that talks have broken down already.
In this age of mass globalisation it is a fact (however unwelcome) that employees cannot entirely dictate terms and conditions to their employers in the same way they could 20 or 30 years ago. No matter how deeply felt the pain and frustration you feel towards BA, the *only* winners in this dispute will be BA's competitiors.
According to the BBC report (online) your terms and conditions are amongst the best in the industry and your employer has already agreed to ensure that they will remain unaffected by the new OS subsidiary - to insist that the "BA family" shouldn't be "broken up" is not going to gain you the sympathy of the public or wash as a reason for striking as it seems no more that trying to ringfence your way of life - a luxury that unfortunately few working people have today (and compared to say losing a manufacturing job without prospect of reemployment...?)
I honestly share the pain of those who are facing a future of uncertainty change (that's most of us at work!) but don't allow the union to back you into a corner and lose what support you do have.
You may win a minor victory by striking - but what then? If you think a strike will stop future changes (both within BA and other airlines), it may be time to question Balpa's handling of OS. To an outsider like me, they seem somewhat out of touch with reality.