To amplify:
Leave Australia: Fill in departure card (required for everyone, Australian or non-Australian), show Australian passport
Arrive UK: Show UK passport, avoid longer queue. No requirement to fill in landing card if you hold a UK passport.
Leave UK: Show Australian passport at check-in (they want to be sure you have right of entry to Australia). No requirement for departure card from UK. No other passport examination when you leave the country.
Arrive Australia: Fill in arrivals card (also required for everyone, Australian or non-Australian), show Australian passport, join shorter queue.