G'day,
Actually it's very simple as long as your licence and medical remain valid in accordance with Oz requirements:
Exercising the privileges of a Non-UK Licence in UK registered aircraft
Article 26, of the ANO 2005, states that a pilot must hold an appropriate licence granted either by the CAA or by a foreign authority and rendered valid under the ANO to fly a UK registered aircraft.
A JAA licence is deemed to be a licence rendered valid under the ANO unless the CAA in the particular case gives direction to the contrary. A JAA licence is a licence issued in accordance with licensing and medical requirements of JAR-FCL by a full JAA Member State that has been recommended for mutual recognition by Central JAA (JAA Headquarters).
A licence issued by any other ICAO Contracting State (including a JAA State that has not yet been recommended for mutual recognition) is also deemed to be valid under the ANO for the purposes of flying a UK registered aircraft, providing that the licence and medical are valid in accordance with the rules/laws of the issuing State, and the CAA does not in the particular case give direction to the contrary. However, the ANO 2005 Article 26 (4) (a) states that the holder of such a licence cannot:
1. Act as a member of the flight crew of any aircraft flying for the purpose of public transport or aerial work or on any flight in respect of which he receives
remuneration for his services as a member of the flight crew; or
2. In the case of a pilot’s licence, to act as a pilot of any aircraft flying in controlled airspace in circumstances requiring compliance with the Instrument Flight Rules or to give any instruction in flying.
I've highlighted the parts which concern you. Basically, if you stick to day VFR private flights in G-reg aircraft, there'll be no worries.
Enjoy!