LBTH says:

The government is considering changing the law on renting homes to modernise and simplify the system, which at the moment is confusing for both landlords and tenants. It has asked the Law Commission to carry out consultation to see what tenants of social landlords, councils and housing associations, think.

The Law Commission is suggesting that one new tenancy agreement should apply for all rented homes of councils and other social landlords.

If this becomes law, then there will be absolutely no difference in rights and security between tenants of the council and tenants of other social landlords. Even if the law does not change, transfers will be set up in such a way that tenants do not lose any rights if they move.

ESG says:

Rents are going to converge so that you will be paying the same rent whether or not you are with a RSL. The difference is that with the RSL you get your property brought up to a decent standard and kept there, whereas with the local authority you might be lucky, or you might not,

Your legal rights as a tenant could be somewhat different with an RSL. But in fact, those aspects of the change of tenancy which might reduce your rights are specifically excluded from the new tenancies.