This is a chimney/flue for the Royal Fusilier's room under the bridge which would have been used by the guards when on duty protecting the Tower of London. The room would have had a coal fire and what we see above on the bridge is the where the smoke would have come out.
The London Clean Air Act came into force on 1956 and smokeless fuel could only be used in urban areas. The staff I spoke to at Tower Bridge think this would have been the end of this room being used.


