After the voyage of Captain James Cook in 1770 in which he charted the Eastern coast of Australia and reported the favorability of this area for colonization, the creation of the colony of New South Wales came about. In 1788 Australia became a penal colony for Great Britain. (e.g. In Great Expectations Victorian writer Charles Dickens's character/convict Magwitch is sent to New South Wales where he becomes a sheep farmer and acquires a small fortune with which he repays the main character's, Pip's, kindness by sending him to London to become a gentleman).
Following the discovery gold and profitable agricultural ventures, other English, Irish, and Scots came to the six British colonies. Then, in 1901 subsequent to the establishment of autonomous parliamentary democracies, a referendum was passed, making Australia a federation. Sadly, before this independence of modern Australia, many Irish Catholics who were sent to the original penal colony were political prisoners and, therefore, held under great suspicion. Consequently, England ordered that they not be allowed to practice Catholicism in order to "improve public morality" and Church of England clergymen were brought in to administer religious and secular instruction.
Although it established its independence from Great Britain and experienced much subjugation prior to this independence, modern Australia remained part of the Commonwealth and still fought on the side of this kingdom in both World War I and World War II, as well as acting as a loyal ally of the U.S. when Imperial Japan attacked in WWII. Ironically, too, it was also in the 1940s that Melbourne, Australia, was voted the safest city in the world.
Australia's close connection to Britain is certainly visible in its flag, which bears a small Union Jack: