The story based in Britain is, as far as I can remember, about a boy who falls asleep on an inflatable tube at sea while on a family holiday to the beach.
He then drifts to a mysterious island whose inhabitants don't know about, or come into contact with, the outside world; he is adopted by the island's chief and his family.
The chief is the main fisherman as the island's hierarchy revolves around fishing.
However the chief's son cannot swim, which leads him to bully the boy as he sees the inflatable tube as the answer to his swimming problem.
The book is at least 40 years old.