sorry J.Bonzo, but Australia was never "part of" Great Britain.
Augsburger is almost correct: the Queen of Australia has other dominions - we are generous enough to share her.
A point of clarification:
the U.K. = United Kingdom, or, in full, the United Kingdom of Great Britain & Northern Ireland.
Great Britain = the sum of England, Wales, and Scotland.
Some people, mostly Welsh & Scots, see Wales & Scotland as being separate countries, but have great difficulty in justifying that view on any basis other than history.