Hi,
You have not advised the nature of source of income in Australia. If the income is from 'non savings income', then you can claim a foreign tax credit of up to 100% of foreign tax paid. You will need to work out your UK tax liability with and without the overseas income. The foreign tax credit will the difference between the two tax liabilities, with the tax credit being up to a maximum of 100% of the overseas tax deducted.
Have a look at HS263 for more information.
Relief for Foreign Tax Paid 2023 (HS263)
Thank you.