Your per diem is paid in cash?? Who still does that?? Maybe when AirNZ replaces its flying boats with those nice new DC-8s, you'll move on to 20th century payment methods too...
But in the meantime, the first rule with cash exchanges is You Can't Win. The second rule is Do As Few Exchanges As Possible. Do you really need to buy sterling? I'd just keep the USD and HKD, take it with me on future trips, and spend it locally (of course, this depends on what you need your money for). If you have a big pile, and you need something in the UK, try and change it in one go when the rate is favourable.
Even better would be to open bank accounts in Hong Kong and the US respectively, and deposit your cash there, making occasional transfers back to the UK. This may not be possible if you are not resident, but perhaps there is a friend or colleague who could help (or even the AirNZ local office)? Another possibility might be to open USD and/or HKG accounts in the UK.
Once you have a local-currency account, your options are much wider. You can use the bank's own transfer facilities (which will probably already be much better than changing cash in the UK), or you can use third-party exchange services such as
www.xe.com, which offer still better rates.
If others have better advice, I'd be most interested myself.