> Uhm, if I remember correctly the UK removed an elected prime minister of Australia
The UK did not, the Governor-General of Australia did. (The Governor-General is the practical head of state, though the Queen of Australia is the formal head of state; removal of a government in response to loss of supply, which had occurred in Australia in 1975, is not irregular in Westminster-style systems whether the head of state of is a monarch acting directly, a monarch acting through an agent like the GG, or elected.)
The UK (both the government and the monarch as monarch of the UK) hadn't had authority (even ceremonial) over Australia for around 4 decades in 1975.
Sorry for my lack of knowledge but from your link it looks like the Governor General John Kerr was a piece of shit (or an idiot at best).
The Wikipedia link makes no mention that I could find of the Buckingham Palace's direct involvement in the constitutional crisis in Australia. What am I missing?
Exactly what happened is somewhat tied up with Australia becoming a republic (https://en.wikipedia.org/wiki/Republicanism_in_Australia). The Dismissal is still somewhat of a sore point for the Labor Party, and discussions of it and its implications to now are common (see https://search-beta.abc.net.au/index.html?siteTitle=news#/?q..., which I'm pretty sure is missing out 90% of the ABC content on the topic, there was a bunch of old archives released last year (2021) which started up the discussions again).
The Australian Govenor-General is an Australian citizen chosen by the Australian Australian prime minister, and acts only on the advice if the prime minister or other ministers, the monarchs role is purely ceremonial.