Two separate conditions have been considered here.
One is the validity of a NZ license for flying UK reg aircraft, the other is the transfer of a rating from a foreign licence to a JAR one.
There seem to be a couple of routes to flying aircraft registered in a State other than the one that issued your license. One is to have your license "rendered valid" by the State of registry of the aircraft, the other is to obtain a full license from the State of registry. As Beagle points out, the CAA will validate a foreign license subject to certain restrictions on what you're allowed to do. If you want those restrictions removed you need to obtain a full license that matches the State of registry. This is of course a generalisation because States will have their own rules on what is and is not allowed.