Think Josh Brolin (US Accent), Simon Pegg (British Accent), Wilfred/Jim Jefferies (Australian Accent).
What is it about the USA that seems to so efficiently strip immigrants of their accent?
Is the US accent just a byproduct of immigrants trying to disguise their heritage?
Is it more Germanic or Irish than British?
Edit: Specificity
An Australian accent sounds absolutely nothing like a "British" accent. At all. I'd argue that an Australian accent is more different to English than an American one is.
How are you defining an American accent, a British accent, and an Australian accent? You're generalising far too much.
To me as a Brit, the Australian accent sounds halfway between a Cockney and an American accent. Also bear in mind Australia itself has regional accents. People from Adelaide supposedly sound quite different (and to my ears, slightly more 'British') to people from other parts of Australia.
I heard (from a source I'm afraid I can't find anymore) that the Australian accent developed in the 19th Century, as immigrants from different parts of the British Isles (including Ireland) settled in Australia, and their children developed a new colonial accent that had elements of all those regional accents, and yet was somehow considered 'purer' than the regional accents it developed from.
Non-Rhoticity, which is the most obvious difference between English in most of England outside the Westcountry and the US outside New England, only developed in England around the late 18th Century, some time after English settlement in the US. Large-scale British settlement in Australia on the other hand only started in the late 18th century, and in fact continues to this day - Australia remains one of the biggest destinations for migrants out of the UK (Spain might have more Brits, but I'm not sure...). Hence why Australian English has non-rhoticity, while most US Englishes don't.
hi! there's a section in the FAQ on American accents ~
as for Australian (and others), here are some more:
How did American and Australian accents develop into their modern forms from their British origins?
Why do Oceanian accents sound closer to British than North American ones?
How did the Australian accent become so differentiated from a typical English accent?
Is the American and Canadian accent the original British accent?