If you mean Private Tenants,No.
What sort of "additional rights" were you thinking of,and why 7 years as a figure?
Our neighbours have been private tenants for 11 years,and do not have any more (or less) rights than when they started their tenancy.
I am sorry to hear that,but a landlord can issue a notice to quit at any time,providing he gives the tenant at least 2 months notice.
I think the 7th Anniversary is just coincidence.