Head to the markets, particularly London Borough market at London bridge station.
A reall good mix of sounds there with all the foreign and local stalls.
For might time, check out Leicester square, you'll get a lot of the typical tourist trap atmosphere with some of the hippy spontaneous drummers after club closing. Some jamaican bands.
http://www.timeout.com/london/thisweek.php
http://www.talentcircle.co.uk/noticeboard.asp
http://www.visitlondon.com/whats_on/browse/spec
http://www.barbican.org.uk/bite/