Jazz Jammin' at UCL - Tuesdays
This is the first jazz jam I went to, back in 2007 where I remember nervously blaring out C minor blues after 10 pints of Guinness.
I must say the quality of music there has massively improved from generic blues to chord-change rich be-bop executed at break-neck speeds!
It starts at 8pm, every Tuesday during term time. On the 3rd floor bar of the UCLU union (25 Gordon Street)
Ronnie Scott's Jazz Jam - Wednesdays
This is every Wednesday in the upstairs bit of Ronnie Scott's. £5 - £10 to get in and the quality of musician is very high.
The jam doesn't start in earnest until about 11pm - midnight as there's a house band (usually very good)
The jam itself is well run, kind of a free for all but with slightly more organisation than usual.
Little Bread Big Jam - Wednesday
A little too far afield for me to go often, but the times I have its been spectacular. Hands down it is the best run jazz jam in London.
The house band plays for an hour then the floor is opened up for a jam, generally a good mix of talents and abilities there. However one time I went there was a tap dancer... I will allow you to draw your own conclusions.
http://lbbjam.wordpress.com/