Home Postcode finder SA Fulham Fulham postcode SA Fulham is a locality in South Australia covered by postcode 5024. Postcode 5024 State or territory South Australia (SA) Region Adelaide Add a free Fulham business listing Be the first listing in Fulham Common questionsWhat is the postcode for Fulham?Fulham, SA has the postcode 5024.What state is Fulham in?Fulham is in South Australia (SA).Does postcode 5024 cover more than one suburb?Yes. Postcode 5024 covers 3 localities, so the postcode alone does not identify Fulham. Browse other postcodes in South Australia, or widen the search to every Australian postcode.