Philip,
Been Bebside-born, the riverside, both banks, was my regular play area.
Still further up the river, from Kitty Brewster, on both sides of the Stone Bridge
( or the "Furnace Bridge" )were walls with metal rings.
Back to hospital angle.... On the 1897 Ordnance Survey map of 1897, 6 " version,
(httm://communities.northumberland.gov.uk/006192FS.htm )
at the top is Infectious Diseases Hospital. To my eye this looks to be in different place to the one on the riverside ?
Michael