Rolling notice clause at lease break

Other

I’m the landlord of a house with tenants who signed on April 1 2021 with a break at 6 months.
I’m going to sell the my property (soon to go on the market) and have proposed to the tenants, by email, that as of October 1 we introduce a rolling 2 month notice period for either party. They have accepted this proposal by email on return.
What do I need to do now?
The AST doesn’t change in any other detail, but I assume I still need to serve the 2 months notice on August 1 (next week) because of the break October 1st. Should I email the 2 months’ notice, adding that we have agreed that they will remain in situ until either party serves 2 months’ notice to end the tenancy.
I’d appreciate your advice and confirmation that this will be suitable to continue the tenancy on this basis, with no need to alter the existing agreement which is the NRLA standard AST. Please
Advise if there is anything additional I need
to set in place.
Kind regards
Jemma Perry (formerly Jemma Page).