It is fine to leave Australia on your Aussie passport and present your UK passport when you arrive. It's common practice for dual nationals.
Upon arrival, join the EU queue. And yes, it will be faster most of the time. They are entitled to ask how long you have been out of the UK and where you have been since you last left.
For your other question: are there any other advantages to having a UK passport once you are landside, the answer is yes. You have 1/2 of the documentation needed to open a bank account for example. You can instruct a solicitor, do business with an auction house, or do any other similar activity where you have to clear money laundering hurdles. You can take out a long-term lease in and around Brum without having to clear immigration hurdles if that's of any use.
Plus if you get stopped by the police and show your UK passports you will not be given 3 days to report to a police station to prove your immigration status.