Oh god, the Competitive Australians rocked up overnight. I used to behave like that. (Australian, have lived in the UK for years but did my time in Brisbane with no car, on the bus route that had the old buses with no aircon, never lived in a house with aircon, etc etc etc, lived in Melbourne during heatwaves and in winter, lived in rural areas so have worked stock in heatwaves, fought bushfires, etc.)
First, I don't think it's controversial to say that Australia is better set up to deal with heat. It's imperfect but it's better, and it's improved even further in the last two decades. And Australians overall know better how to deal with heat and the culture is better at dealing with hot weather.
Second, Queenslanders are bloody brilliant houses for the heat (but terrible in cold weather.)
Third, Australian housing stock is incredibly diverse particularly city by city and state by state but saying it's based on UK housing is really weird to me; yes you'll find houses that have similarities but overall the housing stock is very different. (And I've never been in a McMansion that didn't have aircon.)
Fourth, Australians also complain when temperatures go over 35, despite it being a regular occurrence. And I know quite a lot of people who during major heatwaves kept their kids off school, etc.
I know the Australian superiority thing when looking at the UK dealing with heat is tempting, just like it is for Scandinavian people looking at the UK struggle with properly cold snaps. But it's not actually a game of Who Has It Worse.
Now I'll return to telling my English husband how to do the windows and doors properly for this kind of weather, because he seems unable to learn...