Hi JC
Take a look at these listings:
http://www.jazzinlondon.net/JIL/Dec-11-seq.pdf Most London jazz venues are in there. December is a little quiet on the guitar front but here's a few suggestions.
My pick would be the Peter Ind trio at the 606 Club on Monday 5. Bassist Peter Ind is in his 80s now. He had a long association with Lennie Tristano and has played with Charlie Parker and most jazz legends. It's a guitar/bass piano trio.
David Preston is a great guitarist.
Jim Mullen's organ trio are at the Red Lion in Isleworth on Monday 12 December. That's a bit of a journey out of town though.
On the 15 December, Jim Mullen is playing at a more central pub venue, The King and Queen.
Deidre Cartwright is playing with a group at The Vortex on Wednesday 7.
Nicolas Meier leads a quintet at the 606 Club on Thursday 1.
Antonio Forcione has a run at Pizza Express from 9 to 13, with various lineups.