Sorry to burst your preconceptions, but... no, it isn't. 'Gaol' is barely used in British english outside of affecting an olde-worlde charm for tourists. British usage tends to words like 'prison', 'custody', 'cells', 'remand', 'detention'... barely even use the word 'jail', let alone an archaic spelling of it (and the pretrial/postconviction jail vs. prison distinction common the US system doesn't apply to the terms in the UK). HM Prison Reading might have a sign outside noting that it is the eponymous "Reading Gaol" that Oscar Wilde wrote about, but nobody's calling it that outside of a guidebook.
I think you’re conflating P(Is British|Uses “gaol”) with P(Uses “gaol”|Is British), the latter of which I would expect to be much higher than the former.
(Oh, and to put you out of your misery, a more recent comment by OP contains the clue: "Where I live (Aotearoa)", which suggests they're a New Zealander. So, you missed your guess by around 11,000 miles, and apparently 80 years or so in terms of English language usage.)
