Greg Rusedski got his British Tennis Passport because his mum went to Blackpool once (or something like that).
Seriously, might it not depend upon how the mother came by her British citizenship? If she was born to it there may be one set of rules but the outcome may be different if she was naturalized.
Looking across the Atlantic - Arnie Schwarzenegger is a naturalized septic but that means he can never be President or Vice President.