From To Keep Open and Unenclosed, the Management of the Durdham Down Since 1861, Bristol Branch of the Historical Association, 2005:
On the Avonmouth side of the Pembroke Road shaft two further shafts were made (one vertical to a ventilation turret in the Gulley and the other horizontal to an opening in the face of the Black Rock Quarry.
So, bearing in mind that this is Black Rock Quarry, I'd say there's a good chance this is the third, and least photogenic, ventilation shaft for the Clifton Extension Railway Tunnel. Later on in this wander we'll see the other two, which are rather prettier.
GPS Coordinates:
51.46866, -2.63476
Location: Sneyd Park and the Downs