I got a NZ PPL(A) with Jackie Frame at Hanmer Air in July last year. A small set up but I had a great time and would recommend it to anyone.
You can quite happily fly in the UK in any aircraft that are on your NZ licence with certain restrictions - day, only in UK airspace etc. check out lasors. For example I am rated on C172s and supercubs so can fly these aircraft in the UK.
As for converting, it's simple: less than 100 hours total time you have to take
all the theory exams (including RT and practical), a skills test and get a JAA medical. With more than 100 hours I believe it's just Air Law and Procedures, Human limitations (for some reason, never understood that), and obviously RT and practical. And a skills test and get a JAA medical.
I think there may be somewhere in the North Island that does JAA PPLs, check out the back end of "Pilot".
As has been mentioned before on here, Irv Lee has an excellent site regarding conversions etc:
http://www.higherplane.flyer.co.uk/
hope that helps.