ichkeria, as I recall Australia and New Zealand introduced lockdown on about the same day as Britain, at a time when Britain had already had more than 300 deaths; the other two countries had none, and still have very few.
It seems to me straightforward enough that if the virus is spread by close contact, banning such contact will curb it, and the quicker you curb it, the quicker you stop it in its tracks.
I don't know enough about Peru to know why it hasn't worked, but the BBC says the markets are the big problem: people don't have fridges so they can't stockpile, so they're at risk every day - in other words, the lockdown couldn't be as strict as it was here. The need for crowded public transport, crowded housing, and lack of banking facilities were also cited.
https://www.bbc.co.uk/news/world-latin-america-53150808
but in essence: Peru isn't a first world country. Britain is.