I'm going to check the live version of National Anthem soon. Re: "getting into jazz" and Radiohead, "Life in a Glass House" from Amnesiac contains what AllMusic refers to as "a drunkenly swooning brass band." The band in question is the Humphrey Lyttleton Band, a fairly traditional British combo, with Jimmy Hastings on clarinet. The other players sound like a conventional Dixieland band, but listen to how the clarinet plays under, over, and around the rest of the instruments and Thom Yorke's vocal. It's pure brilliance--jazz or whatever you want to call it.