There are two separate legal issues here.
In the first instance, let's forget about the fact that the householder is council tenant. Any householder can permit anyone to live in a caravan on his property for up to 28 days without requiring planning permission. Beyond that time he'd normally have to apply for planning permission, relating to the change of use for the land upon which the caravan stands. While your question relates to a shed, rather than to a caravan, it's likely that the same legal principles will apply. (i.e. the householder will require planning permission if his guest uses the shed as residential accommodation beyond 28 days).
Having dealt with the rules which apply to all householders, let's now return to the tenant's agreement with his landlord (i.e. the council). Without being able to view the terms of the tenancy agreement it's hard to give a definite opinion. However there will almost certainly be some restrictions written into that agreement, either specifically relating to the use of outbuildings or more generally referring to 'subletting'.
If the guest in the shed has been there (or intends to stay there) for more than a very short period, I have little doubt that the council will take a very dim view of the arrangement.
Chris