Actually the GMB do have a recognition agreement with BA for cabin crew. However it has not been implemented for many, many years there used to be an Air Hostesses Association which was a branch of the GMB and had a seat at the ACC NSP.
Whether they would want to enter the boiler room at the moment is, of course, understandable. I can see a new force emerging at some point in the future be it GMB or PCCC as cabin crew will still need reprentation.
BASSA is a spent force and totally discredited it only needs a little more time for this to sink in.