Just an update... I actually wanted a mobile broadband connection, and 3 said that I needed to buy the actual mobile broadband stick, because apparently putting the SIM into a regular phone would make it run at the casual data rate rather than the mobile broadband plan price (according to the sales guy). I ended up paying £35 for a stick with 3 GB of data.
I also tried O2, which was slightly cheaper, but apparently you need a UK bank account! 😱
So I now have a 3 stick which I probably can't use back in NZ as I'm guessing that it's locked to 3 (and most likely won't be able to connect to the 850 MHz network here either).