Good show,
Hilde at calling up just what icon means.
A visual element seems especially pertinent. And on that ground, I find it difficult to think of a specific book as an icon. A book's aesthetic effect lies in the imagination, formed by the act of reading, rather than in a specific object. A cup of tea is a specific image. The famous London telephone booths are a specific image. Elizabeth I may be said to have become an icon, which is fascinating given how many icons she herself employed in her famous portraits--standing on a map of the world, the orb, etc. Big Ben provides a visual image. Is that last picture of Tolkien, touching the pinus nigra, an icon?
But between an icon and an idol, now there may be more than a few qualitative differences. I sometimes think that Tolkien fans do verge towards idolatry.
But I think you're on to something to suggest the man rather than the book.
A bit surprising that an English site would play so fast and loose with the clarity of the English language--now there you go! Another "icon" for England from one of the new world types.