Notice period

Dear Sir or Madam,
Our tenants who are on a rolling 12 month contract (AST) expiring on 2023 October 1st with 3 month notice period only informed us on 2023 September 1st that they were leaving at the end of the tenancy.
Are they supposed to respect a 1 month notice period or the 3 month notice period that is indicated in the contract?
Reason we ask is that we couldn't find new tenants starting on October 2nd and instead will face few weeks without rent before the new tenants are found.
So not a very useful situation, obviously.
We are wondering whether they breached their notice period commitment but are unsure.
Many thanks.
Best regards,