@eurocelticyankee,
It's kind of funny, but we do have mild accents. South Australians are particularly easy to pick. But.... it's nothing like England - even I can pick a geordie a mile off. Scousers, Lancs, Yorkshire, even Cornwall and Somerset are pretty easy to get.
The US has some pretty distinct accents too. Bahstan, Noo Joisey, all that.
The problem for Australians (apart from relatively few generations of occupation) is we are much more mobile than either the UK or the US. So relatively small proportion stay anywhere near where they grew up. Pre-industrial we wandered aimlessly snapping up land or mining for gold, and post-industrial looking for a better a city or escaping to the country.