The Cooper S was never CKD'd in NZ, always CBU. In fact the New Zealand market was spoilt for choice insofar it was the only place in the world as far as I know where both the English and Australian Cooper S were available new from the agents. A look in a NZ AA motoring magazine from the mid to late '60's makes interesting reading with the Australian and English Cooper S's alongside each other in the new car price lists. I think from memory the Aussie version was slightly more expensive but then again, it was the better car wasn't it?
There were of course both Austin and Morris versions from both countries so you could order one of four variants of the 1275 Cooper S. I think the reality though was it was very hard to get any version so the agents sourced them from wherever they could.
Later on after the Cooper S, the Australian Clubman GT and the English 1275GT were listed together but this time the Aussie version was quite a bit more expensive for obvious reasons.
My particular car was sold new in Queensland ( UK Motors I think, have to check the handbook ) and I imported it into NZ.
