The fellmonger is an ancient occupation and dealt in hides and skins (especially sheep skin) and was also involved in preparation of skins for tanning. The references to a leather trade in Bromley in the trades or professions column of the Bromley parish registers from 1813 would explain why Robert Durling is described as a fell monger.
I first encountered fell mongers in research in Lincolnshire and there is an excellent illustration of local feel mongers at Bourne in the Bourne Archive see Fellmongery in Bourne Licolnshire
The ancient guilds or companies of skinners and glovers were associated with fell mongers who belonged to one of the most ancient guilds or companies and the restrictions that these imposed by their bye laws led in 1835 to the Municipal Corporations Act 1835 (5 7 6 Wm.IV.,c.76.) sometimes known as the Municipal reform Act an Act of Parliament that reformed local government in England and Wales.
The Company of Fellmongers in richmond Yorkshire is a reformed company in recent times and their heritage is described at Company of Fellmongers website