These rims are not interchangeable.  Although either one can be pushed snugly into position, they have incompatible fixing methods.  The ADL rim is secured with a self-threading screw at the bottom.  The Hillman Gazelle rim has only a clip at the bottom because protruding bodywork prevents access to where a screw hole would have been.  This clip is insecure, so some Hillman Gazelles have lost their rims at highway speed.

Both headlight rims appear in the respective Singer Gazelle Parts List books.  However, Singer Gazelles are quite scarce in Australia (relatively few were sold here), so the most likely source of spares would be from wrecked Hillmans.