Fixed term contract - Notice period

I’ve worked at a primary school in England with a fixed term contract for 1 year.

I previously worked at the school through an agency for around 6 months until the assignment ended at the end of the school year, and then in the following September I was taken on as a permanent member of staff.

My fixed term contract (which expired in July) states that my minimum notice period is 3 months but is negotiable with the headteacher.

I’m wondering whether the school can enforce the 3 month notice period even if I am outside the expiry date of the contract?