Lately I've been listening to Mike Chadwick's Saturday evening "Big Easy" programme on JazzFM. It's pretty good.
The "Tremé" TV series is mentioned in dispatches more than a few times but a fair amount of new music gets an airing too.
Here's some Trombone Shorty to maybe whet your appetite (seems Jools is on the case too):
...and then there's also my fledgling Spotify playlist based on music from the show.