Dual UK / NZ citizen living in Australia, can I use my UK passport to leave and re-enter Australia?

The short answer is: with great difficulty.

Leaving Australia

As you state you are "living" in Australia, I assume you entered Australia on your New Zealand passport.

The Australian Government requires airlines departing Australia to check passengers' Australian immigration status using the Advance Passenger Processing (APP) system at check-in. This means you will need to present the passport with which you entered Australia at check-in, in addition to the passport used to enter the destination country (where relevant). See section 3 of this manual for more information on how this works for dual nationals. (This is different from check-in requirements in other countries, where only the passport used to enter the destination country is required.)

Therefore the check-in agent for your departing flight will expect to see your New Zealand passport. If you present your UK passport at check-in, the APP system may return a CONTACT BOC response, unless somehow your UK and New Zealand passports are already "linked" in the APP system. The check-in agent may need to call the Australian Government's Border Operations Centre for special approval before you can board. This is something you will need to consider in light of your circumstances.

Re-entering Australia

In order to re-enter Australia with a UK passport, you need to obtain a visa in advance of travel. For a UK citizen, this typically means a eVisitor (Subclass 651) visa. However:

• you may not be eligible for a eVisitor visa if you have a criminal record. The Department's web site specifically states:

  If you have a criminal conviction in any country, apply for a Visitor visa (subclass 600) instead. If you arrive in Australia on an eVisitor with a criminal conviction, you might be refused entry.

• the eVisitor visa only lets you stay for 3 months, compared to an indefinite stay if you enter using a New Zealand passport.

You can probably leave, although it's possible that the authorities tie your British identity to your New Zealand one and might arrest you and deport you to New Zealand, depending on what you're wanted for.

Returning to Australia on a British passport will require you to get an appropriate visa. You can get an eVisitor visa free of charge from the Department of Home Affairs, but...

Entering Australia this way restricts you to the conditions on your visa. I.e. no work, maximum stay, etc. And...

You should assume that the Australian government knows about the warrant for your arrest. If they can tie your New Zealand passport to your UK one it's quite possible that you won't get the visa.