Children's book about sisters on a fantasy island

The title had the word Gull in. I always think it was called something like "Gull Island" but I can never find a book that fits when searching that. I don't remember too much about the plot but it was two sisters (maybe twins) living on an island society. One of the sisters was very important for some reason in the society, and I'm pretty sure the other sister was the narrator. I think the overarching plot was about a revolution or a nefarious power grab plot.

I read this when I was very young in the early 2000's in England from my local library.

>1 rowanwalker: It's odd, I can't find a book but I find a site sort of describing one, that lists two titles: Island of Seagulls and Gull Island.

Maybe you'll recognize the plot? https://kniga.lv/en/shop/ostrov-chaek/

eta: Oh I also see it as The Lost Conspiracy and Gullstruck Island

Definitely sounds like Gullstruck Island by Frances Hardinge. The older sister is a telepath.