I haven't been to Round Midnight, so I can't confirm what it's like. One of the best know blues venues is the Blues Kitchen in Camden - http://theblueskitchen.com/camden/. If you follow the link you'll see Alvin Youngblood Hart played there. Ronnie Scott's (a jazz club) also has decent blues artists on a regular basis.
You may have already found this site, but it may be of help too - http://www.bluesinlondon.com/gigs.html. Send me a PM with your dates and I'll look at gig listings for that period and see who's playing in the capital while you're here.