Definately open your UK bank account 'before' you leave NZ. This way you can use a NZ utility bill to open it (an HSBC account through HSBC or Thomas Cook or ASB). If you get to the UK and want to open an account you will need a UK utility bill... its a vicious cycle, you need a bank a/c to get a job, but you need a job to get into a flat (to get your name on a utility). You can also open Lloyds TSB accounts through The National Bank, but not sure how much longer this service will last .
The easiest bank a/c I found was through Thomas Cook, opening an HSBC account and I worked for The National Bank at the time!
Also HSBC is probably one of the better UK banks, good ATM's and fees etc.