Were American, Australian, and New Zealand English dialects ever spoken in Britain before the colonization of these lands?
Languages change. Otherwise, we'd still be speaking like Chaucer. The British settlement of America started in the 17th century; there has been lots of time since then for several different American dialects to develop. The British settlement of Australia and New Zealand started over 100 years later, which is why these dialects are closer to those spoken in Britain.
There are aspects of American and Australian dialects which were brought over from England, but which have since been dropped from British English. And there are aspects of American and Australian dialects which developed in the colonies.
The majority of the people who populated Australia and New Zealand (and English South Africa) didn't speak whatever was the RP English of its time anyway (Kentish perhaps), they spoke all different dialects of English including Irish, Scottish, Northern, Western and probably even Brummie.
Imagine all those people stuck together having to converse with each other on a daily basis, they will reach some sort of common dialect over time.
Here's a link to a large number of quite lengthy audio clips of many different British accents http://www.bl.uk/learning/langlit/sounds/
There is some excellent information about* each accent.
*If you listen to the Lerwick Shetland track you can hear 'aboot' for about, Geordies also do that but not Canadians — they say 'aboat'.