While I was in London, I attended an evening of Jazz at the 606 club. I'd highly recommend checking this out - they are a bit hard to find, but well worth it. The web site provides a view of the club, as well as a map to get there. Don't walk by it - the club is located in the basement. You'll walk by what looks like a locked service door. Ring the bell, and someone will answer and let you in.

The food was good, the atmosphere (non-smoking) was appropriate, and the crowd appreciative. Arrive early for a table, the club filled up on the night we were there.