Such terms cannot be introduced like this IMHO. If a working cooker was installed when you took over the tenancy then part of your rent is for this cooker which must be maintained in a serviceable condition by the landlord - in the same way that you rent a telly.
I have inherited some white goods which former tenants cannot be bothered to remove when moving on. They are checked for electrical safety but I always make clear to new tenants that they may have the benefit of them while they continue to work, but should they fail the tenant can either repair them or replace them with their own. Such items are not included on my inventories.
Any information given in this post is based on my personal experience as a landlord, what I have learned from this and other boards and elsewhere. It is not to be relied on. Definitive advice is only available from a Solicitor or other appropriately qualified person.