Hi,
You will need to request a certificate of residence (CoR), in respect of your Australian foreign income. You will need to confirm with the Australian tax office, which of their forms you will need to complete to request that no tax is deducted from your employment income.
The CoR will show that you are resident in the UK for tax purposes.
You will need to register for Self Assessment, if you are not already registered, so that you can declare your foreign employment income.
Check how to register for Self Assessment
Thank you.