Firstly may I apologise to all that I have not had an opportunity to post an earlier response. I am afraid I forgot the password and there are so many of those passwords to remember these day.
I do not propose to respond to all the posts. I will simply focus on the original question. This says that in effect the tenant has been trying get her son "as a succession" on her tenancy. The terminology that has been used is somewhat confusing but I am assuming that you are trying to establish now with the Council that in the event that your mother passed away, you will be treated as a successor to the tenancy. It may well be that your mother is trying to assign the tenancy to you in her lifetime.
A person who is a member of the tenant's family is qualified to succeed to a secure tenancy provided they have resided with the tenant at the premises as their principal or only home for a period of 12months ending with the tenant's death.
As a matter of law, the burden is on the person who claims to succeed to prove that they are entitled to succeed. The Council does not need to prove anything and the Council is right to require proof of residence at the property for the relevant period. That proof of evidence need not be a bank statement but the potential successor will need to provide other evidence such as driving licence, utility bills etc.
Even if the potential successor actually succeeds to the tenancy, where there is under occupation, the Council can seek possession of the premises but it will have to be show that there is suitable alternative accommodation available and that it is reasonable for the court to make an order for possession. In dealing with the issue of reasonableness, the court will consider all relevant circumstances at the date of the hearing of the claim for possession. The question of reasonableness is a matter for the court based on its findings on the evidence presented to it by both the Council and the tenant.
Therefore even if the Council have told the tenant that the potential successor will have to move to smaller accommodation, ultimately, that decision is for the court to make in the event that the Council seeks possession.
It is stated that the Council are "trying to say (but won't admit it) that the original secure tenancy does not apply anymore". Provided the tenant resides at the premises as their only or principal home then the tenancy is a secure tenancy and there is no question of the secure tenancy not applying any more. Even if the tenant was or is the subject of a suspended possession order which they have breached, changes introduced by the Housing and Regeneration Act 2008 means that the secure tenancy continues irrespective of any such breach and the secure tenancy only ends when the tenant is evicted.
The potential successor and the tenant should seek further advice on the possibility of the tenancy being assigned to the potential successor. This is permitted by section 91(3)(c) of Housing Act 1985 and I do not believe that the under occupation provisions in the Housing Act 1985 applies to an assignment to a potential successor.