Trying to assign a single cultural identity to the citizens of Australia is an impossible task both for geographical and historical reasons:
First of all, geography: Consider the size of Europe. Yes, everything from Greece up to Iceland. Then add 50% to that size. Now you've got the size of Australia. It's a BIG place. (It's as far from Adelaide to the next town or city of any reasonable size as it is from London to North Africa). In the UK there are vastly different cultures in London, Bradford, Edinburgh and Belfast, so it's obvious that anywhere as big as Oz can't really have a unified culture.
Secondly, history: Many people in the UK still think of Australia as a country populated almost exclusively by descendants of British settlers. The reality is that, for the past 50 years, most Australian immigrants have arrived from South-East Asia. This has made many parts of Australia a multicultural society (although racism, both against Asians and aboriginals, certainly exists within some sectors of Australian society).
If you visit Oz, you'll find all types of people and a wealth of different cultures. Brits normally feel very much 'at home' in Oz (despite the number of 'pommy' jokes!) but there are a few obvious differences. (The most notable is probably a lack of 'formality'. Expect the bank cashiers to be wearing shorts and T-shirts and to address you by your first name, for example).
Chris