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You have a good memory that was ages ago! I live there so it was a very easy one for me.
Technically the B&H boundary to the east is longridge ave in saltdean and approx the Sussex beds shop in portslade to the west. I only know this due to working for the soul sucking council and arguing the toss over who should accept responsibility for things between councils. Super boring but I knows my boundary lines.
@Dogtemple once sent me out to Rottingdean, and I got soaked! It was still fun.