UK Citizen, currently living in Australia - how to apply for L type Visa?

Christina, personally, I think you can apply for it from Australia.
You should prepare those documents first containing your passport and its photocopy, the application form and a recently-taken passport-style photo, your valid entry permit to Australia, as well as hotel booking record and round trip air tickets for China. And then submit your application to the CVASC to apply for it.