The Australian Government signed and agreement with the UK (and a few other countries) for reciprocal health care and this entitles you to limited subsidised medical care where it is considered medically necessary (for most everyday visits).
When you arrive, make sure you visit your local Medicare office and sign yourself and accompanying family up for medicare assistance. It costs nothing to sign up and unless you have done so you will be paying privately for whatever services you receive. There are some medical procedures or facilities (such as counselling) that you may have to pay out for at first but more often than not you can clam a portion of the fee back by visiting your local Medicare office (and presenting any receipts for payment - so make sure you keep them safe).
You should try to enrol yourself (and family) into a doctors surgery in your area that 'bulk bills' as you could otherwise be paying around $65.00 per visit and (usually) per person.