I like most styles of jazz, but I'm not fanatical about anything such that I study and can speak authoritatively on it. So sorry, no suggestions, but others seem to know more anyway :-)
But to ramble on as usual: I used to live in Ealing and almost always went to the annual free Jazz Festival there. Not as good as it used to be though, cut down in hours/days, and now they charge to enter the walled off bit. Time was when one could buy a reasonably priced ticket to get to the front seats away from those who just wished to chat and picnic their way through the performances, but the prices rose and now there is no ticketed front bit, so you take your chances on getting a good seat. Easier when not on your own as someone can always fight off others who want the seats you've grabbed while another goes to the bar or food stalls.