I don't think they could go to Small Claims Court (but not a lawyer so happily corrected) as I don't think you are obliged to take up travel that you have paid for.
I think the biggest 'stick' BA have is revoking your BAEC account though I am not sure if this has happened.
I know people have been charged for a 'stop-over' in LHR in order to only have their bag checked to LHR rather than the final destination. That clearly happened at check-in rather than after the event though.