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Euler diagram of the terminology of the British Isles
(lemmy.sdf.org)
Apologies. This might not be the perfect community for the post.
"British and Irish Isles" is the most common descriptor for the whole archipelago I see, and it seems a fair one even if it's a bit long. It'd be nice if we could all agree on something catchier but that seems unlikely, all things considered
Gaelic Isles
Celtic would be better. Gaelic literally means coming from the Gaels, aka the Irish. Welsh and Cornish are Brythonic language speakers, not Goidelic/Gaelic, but they are all Celtic languages. The Angles, Saxons, Frisians and Jutes invaded Celtic Britain starting in the 400s.