Australian English has branched off from British English. A while back, there were two main varieties of pronunciation in Australia, the Received Pronounciation (British), and the Broad Australian Accent (the very stereotypical seen in movies). The "General Australian" accent is a combination of the two, the middle ground between the accents.

Australian English shares a lot with British English, but has its own unique elements, (e.g. Australian Diminutives like 'mozzie' for mosquito, and 'arvo' for afternoon)

With Americanization in media, American Slang is being transferred to the rest of the world, including Australia.

Note: Australian English stems from British English, and is not a crossbreed between American and British. You could think of it as a 'modified' British variety, with a few Americanizations.

To me, Aussie English is as different from British English as American English is. And South African English is, too. Each sector of the English speaking population on this planet has a different experience, a different culture and a different way of expressing themselves with language. Yes, we have a similar basic vocabulary. That's what makes it English. But our slang and accent make it all different, too. The only thing that makes Aussie a little closer to British English is that the Aussies have adopted a little bit more of the British slang. Personally, I have no difficulty in distinguishing Aussie from British from South African English. It's all a matter of listening carefully.