Hi Neoaus,
Please see Article 6 of the DTA
UK/ AUSTRALIA DOUBLE TAXATION CONVENTION
As a UK resident, the UK has taxing rights on your worldwide income.
If tax was deducted on this income in Australia, then you would be able to claim foreign tax credit relief on this, to stop you being taxed on it twice.
As you state no tax is paid in Australia, then it is correctly taxed in the UK and no refund can be claimed.
Thank you.