I believe the stereotypical neutral British English accent is known as RP (Received Pronounciation) or "BBC English" - the kind that BBC TV & radio reporters from decades ago were required to speak in.
So it's still fair to say "British accent" based on what seems to be the usual we hear. In Oz, there are very minor differences in the various states but it's pretty uniform. The main difference is the range from neutral to very broad.
Not just that, in Australian English there are various Ethnolects formed in various diasporas and the occasional speaker of the "posh"/"Cultivated" Australian accent.