F.a.m

Hi everyone.... I recently had approval of Australian citizenship, but still waiting to receive a letter of invitation from my local council for my citizenship ceremony. I will be traveling back to the UK in September for a month, can I still travel on my UK passport or do I need to apply for a Aussie passport and use that passport from now on? Also if I have both a UK and Australian passport, can I leave Australia on the Australian passport and then enter the UK on my UK passport and do it the other way round when returning to Australia. Any help out there would be great. Thanks Fernando.