Hey, I moved to NZ just over 2 years ago. A friend (still in the UK) pointed me at this thread (the only reason I joined this forum) in case I could offer some advice.
800 (~1600NZD) GBP is about what you can expect to pay to get your bike over from GB. As a new immigrant you can import one vehicle GST (VAT) free. GST is currently 15%, and will be calculated on the specified market value of your bike on import. You're allowed to sell your bike at any point once you're here, no restrictions, but be aware that you'll have to pay any outstanding GST at the point that you sell - if your bike is worth $6000 (3000 GBP) on import, you'll save $900 when you import it. If you sell it after one year, you'll have to pay $450 outstanding GST. If your sell it after 2 years, you'll have to pay zero GST.
What's it like to ride over here? The roads are quite literally empty. NZ is a population of 4 million, 3 million of which live in the North Island. Even in the North Island, around the Wellington (Capital) region my friends and I can ride for a full day and see maybe 10 other vehicles. No joke. And the roads are generally good.
Having said that, once you get off the main drag there are many, many, gravel roads, especially if you want to reach the non-tourist (80%) coast lines, or enjoy most of the country's interior areas.
In the UK I had an FZ6 only. Here I have a BMW R1200GS, a Suzuki DR650 (used almost exclusively for off-road - and getting there and back) and my imported FZ6. The ability to ride off-road totally unrestricted is an opportunity not to be missed, as is the opportunity to ride so many gravel roads.
If you ride only a road bike in this country you're 80% wasting your time. I've used my FZ6 once in 8 months. Don't get me wrong the road riding is awesome here, infinitely better than the UK, but you'll see a tiny fraction of the NZ you could otherwise see if that's what you restrict yourselves to.
Bikes here, either new or used, cost a good deal more than in the UK, so if you do bring your bike you can easily sell it for more dollars than in the UK (bearing in mind the GST implications), and could easily recoup the import cost. However it can be a pain in the arse to get the bike here in the first place. I used James Cargo and that was not without significant problems. I won't bad-mouth them because they came good in the end, but suffice to say it was more stressful than it needed to be.
Having gone through the process I'd whole-hearteadly say sell your bike before you come here. Accept the higher cost of bike purchase here, and get a bike that can take you anywhere and everywhere. You will not regret it, in fact it will be something you celebrate... ...daily.
If you really do want to discuss in detail, let me know.
Ian.