"Succession
Transfer of tenancy to someone else
On death of a tenant, the spouse or partner may have the right to take over the tenancy, as long as they have been living at the property for the last twelve months. This is called succession and, by law, succession to a tenancy can only happen once.
If a tenancy started on or before 31st March 2012 and the tenant passes away, another member of the tenant’s family, who has also lived at the property for the preceding twelve months, may qualify to succeed, if there is no spouse or partner.
However, there are new rules from April 2012 regarding succession, which only allows the spouse or partner to succeed to a tenancy that started on or after 1st April 2012. If there is no surviving spouse or partner, a succession will not take place. In these circumstances, if you are living in the deceased tenant’s property, you should seek advice from your Area Housing Manager about your housing options."
That's from Winchester city council, but it refers to the law, so is likely to be country wide.