As for SOSR, it would be in the airlines' interest that this was not instigated, however if this latest offer is rejected then a 90 day notice of new contracts may be applied. (Using the contract already signed by the non union cabin crew)
I don't think BA will use SOSR as they already have what they want, with the notable exception of an end to the dispute. However, if they do use SOSR, I suspect they will be a little more radical than the contract of the non-union crew contract. I suspect a lot more clauses will appear in the contract. One of the main benefits of using SOSR to change contracts is that it would invalidate the current union recognition agreement and open the door for BASSA's demise.