@Mike344
No it doesnt. RRA specifies the 2 months IF not already agreed between LL and tenant. It can be less. This is the official guidance
"If your tenancy agreement does not say how much notice you must give, you need to give at least 2 months’ notice.”
Assured periodic tenancies: a guide for tenants: How to end your tenancy - GOV.UK
Tenant can give as much notice as they like. RRA is about how much can be required by LL in tenancy agreement
Notice can be given any time but the final date is the last day of a rental period. (So if that is from 1st of month and tenant give notice on 2nd, they may have to give just under 3 months notice)
More detail from "independent landlord " below
Good luck
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See eg
“If your tenancy agreement does not say how much notice you must give, you need to give at least 2 months’ notice.”
Assured periodic tenancies: a guide for tenants: How to end your tenancy - GOV.UK
"
How much notice does a tenant need to give to end a tenancy?
Under the rules introduced by the Renters’ Rights Act, a tenant must give at least two months’ written notice to end an assured periodic tenancy, with the notice expiring “so the tenancy ends on a day when the rent is due or the day before the rent is due” (to quote Government guidance for tenants).
A landlord cannot require a notice period that exceeds two months, but can agree to a shorter notice period (see** Section 20 RRA**). For example, if the tenancy agreement refers to a shorter period, such as one month, that will prevail.
Tenants should check the tenancy agreement to see whether the notice period is shorter – many tenancy agreements require one calendar month. If so, the tenant only needs to give that shorter period of notice.
Tenants need to tell landlords formally if they want to end a tenancy agreement. It needs to be in writing, and must be for the correct notice period. Do allow plenty of time for the notice to be served if serving it by post."
Tenant notice to quit rules with free template • The Independent Landlord