When a Brit retires in Australia, as a resident, and has a UK pension, either State or Private, this will be taxed in Australia. (The same as any other income).
To ensure that this income is NOT taxed in BOTH countries, you must advise the British Tax Authority (HMRC) of the situation.
As at April 2014 the correct form to use is:
Form Australia-Individual 2003 – United Kingdom/Australia Double Taxation Convention (SI 2003 Number 3199)
or for those in neighbouring New Zealand:
The main HMRC page for this information is: