Firstly, the UK response has been terrible, Australia far better.

However there are several contributing factors and it certainly doesn’t come down to mask use as the primary one as mask discipline in the UK hasn’t been bad in my experience.

This is a seasonal disease (the main reason for the UK summer reprieve), and it’s now summer in Australia, and they have also been far better at quarantines and contact tracing and have used this period wisely to get the disease under control. All these factors matter in a response, and the UK has suffered from panic management and a lack of difficult measures at the right time and is now entering the peak season for this sort of virus so things will get worse for a month or two at least, even with a new lockdown.

> What worked in Melbourne was that 8 months of house arrest for everyone living in the city...

The .au epidemiologists I've heard on NPR have made it clear that what worked in Melbourne was everything they did, including a lockdown and including contact tracing.

I'm not sure that's completely fair. Countries vary so much that putting it down to "the government" ignores all the other factors. You're examples are all on the southern hemisphere, with mostly nice weather where people spend more time outside. General population health also has a massive effect. Here in the UK we are a nation of overweight old people, but fat-shaming is a thing so that's only going to get worse.