Are there any offices of any New Zealand Banks in London UK?

Answer 1

You typically have to be NZ resident to open an account at a NZ Bank.

Do you actually need a NZ Bank ? - chances are your UK Bank has a NZ branch ... check out first link for Banks registered in NZ.

Do you actually need a branch ? - most Banks offfer an Internet option .. this can be used to transfer funds between Banks (check out BNZ 2nd link)