The Occupiers' Liability Act 1957 placed a duty of care on the occupier of any land or premises over anybody lawfully present (i.e. visitors). This duty of care was extended by the Occupiers' Liability Act 1984 to include all persons, whether present lawfully or not (i.e. including trespassers).
Whilst it appears that the resident is an occupier in this situation, it would be for the courts to determine whether the Council remains an occupier, assuming that it owns the land in question, due to the informal and undocumented nature of the arrangement. If the resident has an accident within this ill-defined garden extension, the Council could be liable, however perverse that may seem.
My advice, as in all such cases, is to formalise the tenancy, by whatever means the Council deems appropriate.