Australia's low COVID rates can be explained by three factors: always locking down until zero community cases are reached, having no land borders and enforcing a hardcore quarantine on all arrivals. Lets compare them to the UK to see why one failed to achieve while the other succeeded.

Lock down until zero cases

Australia's general modus operandi has been to clamp down on all in-person activity (including a ban on protesting and harassment of people sharing family photos) until zero community cases are reached. Not a "low amount", not "enough to relieve the hospitals", but zero. One single case can grow into thousands and then into millions (in fact, the original COVID infection probably happened to a single person) so you can't tolerate a single infection in the community without some hardcore measures. As a result, Melbourne has been in lockdown for 111 days during their "second wave" and then spent a couple of weeks in lockdown recently over a few local cases.

To contrast this, the UK never reached zero cases since the initial wave started in March 2020. So essentially their lockdown was pretty much a waste of time, short of relieving some stress from their hospital system. Otherwise it merely delayed the inevitable as cases avoid in spring 2020 came back roaring in the winter.

No land borders

Australia is a relatively remote island where everyone has to arrive either by ship or by plane. This makes border control a no-brainer as you just have to ensure quarantine protocols in your airports and sea ports. Obviously a rogue traveler could in theory charter a boat and land on a beach in the middle of nowhere but that's something out of reach for the vast majority of people.

Now you might argue that the UK is likewise an island (along with Ireland) and that all sea crossings are controlled but there's one huge difference: truck drivers. As a general rule truck drivers take their goods from one country, drive straight into another country and then unload them at the destination. This is in contrast with ships or planes where the cargo is unloaded at the port and then carried on to the destination by local residents. So even if the UK was absolutely perfect in securing their borders, they would still have to contend with the problem of tens of thousands of foreigners coming in without quarantine. In theory you could build a system where all trucks unload their cargo in, say, Dover and then local truck drivers carry them on, but this would take many years if not decades to complete. Stopping trucks altogether is not an option as this would cause massive disruption in the supply chain.

Hardcore quarantine

Four types of border control were seen during the pandemic:

1. "Free for all" - seen in Mexico, Turkey, Brazil and a few other nations. Anyone could come in with no quarantine, though sometimes a test was required for entry.
2. "Only locals" - free entry with no quarantine if you're a citizen/resident, otherwise you're banned. Implemented by the US.
3. "Home quarantine" - after entering the country travelers are legally obligated to stay at home for 7-14 days and sometimes obligated to get tested on arrival. Implemented by most countries in the world, including the UK.
4. "Hotel quarantine" - armed men escort all arrivals into specially designated hotels with no one allowed to go out before they spend 14 days in isolation and get multiple tests. Implemented by China, Taiwan, Australia, New Zealand

Is #3 as good as #4? No, definitely not. Lets evaluate each solution as to how well it can stop the virus:

1. Allows for at least 1 infected person to interact with the general public upon arrival
2. Allows for at least 1 infected person to interact with the general public upon arrival
3. Allows for at least 1 infected person to interact with the general public upon arrival
4. Does not allow any arrivals to interact with the general public

Is it weird that 1-3 are all the same? No, because remember once again that one case can easily grow into millions. There's no such thing as "good enough" when it comes to international quarantine, it has to be all or nothing. And you definitely can't pretend that the locals are all virus-free while the foreigners are all infested with COVID, as the virus does not discriminate by ones citizenship.

Australia took this one step further by preventing citizens from leaving the country, which reduced the number of international arrivals. They've also introduced a complete ban on travel from India for a few weeks, which applied even to citizens.

As a final note, its important to distinguish between "success in fighting COVID" and "long term success". It remains to be seen if Australia can reopen the border after their vaccination campaign is complete. Its possible that they will spend many more years in a border lockdown due to strong fear of the virus and its many variants. In contrast the UK is likely to fully reopen sometime this year and just carry on with life while accepting a certain number of COVID deaths per year as unavoidable. Which scenario is a better solution still remains to be seen,.