I don't think this is a British condition but more a human condition. I was, however, thinking before I got to Shepherdlass' remarks, and Lancashire Lad and Elmer Fudd, that I would rather see some input on what are some of the features that make someone (anyone) seem iconic in their field to those of us who love their field?
I suspect, for me at least, passion is a necessary ingredient.
As Art suggests, longevity.
Influence on others in the field; inspiring "I wish I could be more like ___." This is not the same as inspiring copycat performers, which cannot possibly be as good as whoever they try to copy, but a more general approach: wish I had Pete Seeger's passion for his causes, Gordon Bok's poetic introspection, Bob Dylan's ability to try something never tried before, Art Thieme's shoot-from-the-hip wit, and many more. . . .