Can I apply for business visa in Sydney with a UK passport?

According to the official website of the CVASC in Sydney, you can apply for it. But you need to submit your electronic visa. Australian entry record (stamp) should be provided, both the original and the copy. However, new entry and exit administration regulations on foreigners were put into use on July 1. Some new changes have occured. You might apply there but it's difficult to say whether you will get it successfully.