The density of cities in australia and NZ are somewhat similar to european cities. The sparseness of Aus and NS are because their population is concentrated in cities, and there are large land masses.
If the US or UK wants to, they can certainly make the same sort of lockdown. There are costs to it, but the leadership being incompetent at actually leading, is a bigger roadblock over the cost.
The US could never do it because the federal government does not have that authority. They have lacked leadership, but they were also uniquely positioned for a world of hurt going into this.
The UK is doing about as well as similarly populous countries nearby. Which is to say, not well at all.
UK has a population of 60 million. Australia is 25 million. Both are a set of islands.
Not exactly an order of magnitude difference in population but yet there is a massive difference in the strategies and polices they've deployed. And now UK is a complete mess heading into winter and Australia has effective elimination.
I am in the part of Australia that didn't eliminate it well before winter. But with 112 days of lock-down _during_ winter we certainly had the numbers come down dramatically and have had twenty-three days so far of no new infections or deaths.
From tomorrow we no longer have to wear masks outside unless it gets crowded such that you cannot maintain physical distancing!
The UK is also next to Europe and a travel and business hub for the world. Australia is next to nothing important and has far less travel to and from the rest of the world.
If the US or UK wants to, they can certainly make the same sort of lockdown. There are costs to it, but the leadership being incompetent at actually leading, is a bigger roadblock over the cost.