Have you looked up Granny's birth cert on Freebmd?
Even just the indexes should tell you whether it was Battle Sussex or Battle Reading she was born in. You never gave us her name, otherwise one of us would have done it for you.
Battle Sussex by the way also had a 'House of Correction' with 6 cells which was connected to the police station. She may have been a traveller and for convenience sake underwent the birth in there. Unfortunately, the lack of names, ages and some indication of social standing, often hampers our attempts to be helpful.
Roy G