I left Australia on my British passport and entered Ireland on my British one. I have misplaced my British passport and am travelling to England from Dublin tomorrow, can I travel there on my Australian Passport? There are no stamps in my Australian passport.
You might have an issue further down the track if/when you enter Australia again. Australian immigration always say that a person who holds an Australian passport should leave and enter Australia using their Australian passport - but once out you can travel on any other you may have.
It's always best to leave & enter a country you hold a passport for by using the passport for that country (or the "best" passport - e.g. the British for any EU country, the Australian for New Zealand).