It's the home of the Avon Wildlife Trust now, but back in the day it was Brandon Hill Police Station. It's marked on maps as recent as the 1950s Bristol Town Plans. An interesting tidbit from Bristol Then and Now on Facebook:
One of the first police stations in Bristol, it was opened in 1836 - policemen from the station used the building housing the Jacob's Well as a bicycle store and many old bicycle lamp batteries were found in excavating the small entrance to the mikveh. The Police Station closed in 1967 and it is now the base of Avon Wildlife Trust.
GPS Coordinates:
51.45299, -2.60962
Location: Cliftonwood