Bill Caddick wrote John O'Dreams. And I'd say he counts as English.

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There's no suggestion in the Ossian books, "Folksongs and Ballads Popular in Ireland"(which note him as the author) that this is an Irish song, except by the adoption process in which any good song is allowed to immigrate and get naturalised.

No more Irish than the Wild Rover or No Man's Land, and no less either.

And no less American either I'd be inclined to say.