Other responders have addressed the need for acute care.
It's probably worth saying that you'd be entitled to care on the same basis as a UK resident, so
I wouldn't dream of going to Australia without good travel insurance, and I suspect you should get insurance before coming to the UK, unless the costs of repatriation are not an issue to you. The good news would be that as you're covered for acute care by the public system, the cost of such insurance should be significantly less than if you were going to a country without a reciprocal care arrangement, or to the USA.
I guess the other thing to consider is you're probably not flying directly from Australia to the UK. What would happen if you became ill en route? Another reason to have good insurance.