If a contract can be terminated by notice can it be a fixed-term contract?

Yes. If in the normal course of events it will continue until the date specified, a contract for a fixed period that can be terminated earlier by notice is still a fixed-term contract for the purposes of the Fixed-term Employees (Prevention of Less Favourable Treatment) Regulations 2002 (SI 2002/2034).

In Allen v National Australia Group Europe Ltd [2004] IRLR 847 EAT the employee was employed on a fixed-term contract with an expiry date of July 2003 and an additional clause stating that during the first six months of service either party could terminate the contract by giving one week's notice. When the employer dismissed Allen on grounds of competence in January 2003, but without giving him the opportunity to access the performance improvement procedure, he claimed that he had been discriminated against contrary to the Regulations. The Employment Appeal Tribunal held that he was a fixed-term worker; the provision for earlier notice did not negate the fact that the original intention of the contract had been that it would be seen through to the end of the fixed term, unless an event occurred that was not in the normal course.