You may have been looking in the wrong section (section C - PPL).
Under JAR-FCL, you can only renew a license if you have a valid class rating. So first and foremost you've got to renew your SEP(land) class rating. Info in section F1.5.
There is an interesting provision there:
Where an applicant can show that they are currently
flying under the privileges of an ICAO licence, and
are flying the same aircraft type/class within their UK
or JAR-FCL licence, the renewal requirements will
be based on the expiry date of the rating currently
being exercised.
So you do need to do a skills test in any case. But this provision might save you some money since the examiner may legally renew your SEP rating, instead of having to send it off to the CAA. But to be honest, straight after this you'll need to send things to the CAA in any case, to renew your PPL. See section C5 for that.
Alternatively, have you considered flying a G-reg within the UK on your AUS license?