I am currently living in melbourne and the price of flight training over here is about the same as the UK.
I assume that's Melbourne, Australia and not Melbourne, Florida, USA, is it? Because there are several JAA flight schools in Florida so you can get the PPL over there. In fact, in Sebastian, just a few miles south of Melbourne FL there's an instructor associated with OFT running his own little OFT branch office.
Anyway...
An AUS PPL or a JAA PPL... It depends on what you want to do and where you want to do it. An AUS PPL, being an ICAO PPL, is either implicitly, or easily "rendered valid" in other ICAO countries and generally gives you privileges in that country up to the level of a PPL from that country. If your only intention is to fly for fun, in Day VFR conditions within the UK then your AUS PPL is as good as anything.
A slightly more complex issue would be your medical though. I simply do not know if an AUS PPL plus a JAA class II medical is enough to get you flying in the UK. If not, then you need to find a way to keep your AUS medical up to date in Europe.
A JAA PPL is less of a hassle in JAA land since international flying requires less paperwork and you can far more easily add things like an IMC, IR or other things to it.
You can do all your flying training in JAA land and get a JAA PPL. But it is also possible to do large parts of your flying training in AUS. Have the instructor properly sign off your logbook, make sure you bring your student folder over to the UK with all the "instruction complete" marks next to all flight exercises, bring a copy of the instructors licenses (as they will not be known to the CAA, obviously) and you should be able to count those hours towards the 45 hours requirement from the JAA (and all its subrequirements).
Upon arrival in the UK, you "only" need to do the seven theory exams, the R/T practical, a few hours aircraft and airspace familiarity and then the skills test.
So you can start your training in AUS, and finish it whenever you get to the UK.
(Having said all this, it would be a good idea to contact the UK school where you intend to finish your training and see what sort of paperwork they exactly require for this to work.)