Further to my comment and @Annoyed's answer -
Here's what Smartraveller (the Australian government's travel advice site) says,
If you hold another country's passport, seek advice about how it should be used. Take your Australian passport and use it to depart from and return to Australia. An Australian citizen cannot be granted a visa for Australia.
When entering Australia, all Australians, including those who hold dual nationality, must be able to prove that they are an Australian citizen. An Australian passport is conclusive evidence of a person's identity and citizenship and provides the holder with right of entry to Australia.
An Australian citizen who arrives without an Australian passport may be delayed until their identity and claims to enter Australia have been checked. If a foreign passport holder claims to be an Australian citizen, immigration officers must confirm and verify this through official databases, which will cause delays.
International airlines have an obligation to ensure that they only carry appropriately documented passengers to Australia. In the absence of an Australian passport, airlines are unable to verify a claim of Australian citizenship at the time of check-in and may refuse boarding. The airline may have to make inquiries with the Department of Immigration and Border Protection in Australia seeking approval to carry the passenger, which takes time and may cause delays.
If I were you, assuming you're eligible, I'd try and apply for an eVisitor visa using your British passport to prove to the airline that you're eligible for entry into Australia (even though the quote above says Australians cannot be granted a visa). It's free anyway and if you don't need it on arrival, they'll probably cancel it for you. See here for more details on the visa - http://www.uk.embassy.gov.au/lhlh/IMMI_holiday_info_eng.html
I'm not sure how you'll leave Australia though, as you might have issues if you enter using your expired Australian passport, then try to leave using your UK passport. Maybe you could have another chat with them on the way out :)
As with most immigration questions, you should confirm this with the authorities to be sure. See http://www.uk.embassy.gov.au/lhlh/aboutus.html for contact details (they also have a Twitter account at https://twitter.com/AusHouseLondon but I probably wouldn't try that if I was pressed for time).
The easiest option, if you have 3 working days in London or Australia, is to apply for a new Australian passport with priority processing. Do it in London to make things easy getting to Australia and back; do it in Australia to make things easy when you leave.
Priority processing fee
Note: Available to eligible clients in Australia, London and Washington. Payment guarantees issue of a travel document within two working days of receipt of the application and all necessary information at the passport office. You should allow extra time for your application to reach us by mail and for your passport to be returned to you by registered mail (unless you arrange to lodge and collect it personally).