Thanks for your question - I am Sam and I am one of the UK tax experts here on Just Answer.
If you own any other property then the additional 3% surcharge will arise on this purchase. If you do not then there will just be the basic charge arising.
If you are paid rent - then as this income arises in the UK you will have to register with HMRC for rental income and complete a self assessment tax return each year to declare the rental income and associated expenses.
Link here to register for self assessment
But as you will be anon resident landlord then you will eitehr apply for the NOn Resident Landlord scheme (allowing you to have your rents paid free of tax deduction throughout the year) or your parents (as your tenants) will need to deduct tax and pay this over to HMRC
Link here re Non Resident landlords
As you are a UK citizen you will remin entitled to UK personal tax allowances, which may then render you NOT having any UK tax liability.
But you also will need to declare this income to the Australian tax authorities but can also claim any UK tax suffered (which may be NIL due to your entitlement to UK personal tax allowances)
If you are not paid any rent - then you have nothing to declare either in the UK or in Australia.
Your parents will be the ones who pay council tax, as they are the ones who will live in this property - along with all other utility bills so there are no other fees that arise through this process (other than legal fees to manage the purchase of course)
Your only other consideration would be making sure your bank are aware of any large transfer - and discussing this with them prior to the transfer, and any charges your bank in Australia would charge for this transfer.
Let me know if I can assist further - or if you have all that you need, then it would be appreciated if you could rate me for the level of service I have provided (or click accept)