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.
Regarding the UK, is 1975 the last instance of such a thing? That's quite a while ago.
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?
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.