PA28,
If you want to fly in the UK, you'll almost certainly need a JAR license. That means training in Europe, or at least at a school approved by a JAR Authority.
As far as I know, the only JAR Authority to approve any school outside Europe is the UK CAA. The complete list of approved schools is
here. Unless it's changed since I last looked, there are no approved schools in Australia, so out of your choice of Australia/America, that restricts you to America.
The other alternative is to get an ICAO license anywhere in the world, then convert it to JAR - but that's a very long/expensive process, and probably not the best way for you to go.
If you particularly want to fly in Australia then bear in mind that you will need to do some hour-building at some point, and you can do this anywhere you like - there's no need to stick to an approved school. So you may be able to hour-build in Australia, then do your CPL and IR (or at least most of the IR - you'll need to finish it in the UK) in the US.
FFF
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