Some people who like jazz have a collective name for themselves but it tends to be Jazzers rather than Jazzies.

By the way the song Monto which Gulliver mentions above was written by George D Hodnett (GDH) who was mostly a Jazzer and wrote it as a bit of a slag on folk music. Strange that it should be mentioned as the epitome of Trad by whoever was making the snide remarks on the Radio.

Of course by some definitions Monto can never become trad. because its authorship is known.