Yes, there is a general IT recycling place, not SE1 but not far from there off the New Kent Road:
OFFERS / Ex-IT
7-9 Brandon Street, Southwark, London, SE17 1NA, 0207 703 5222, firstname.lastname@example.org, http://www.crispej.org.uk/
(I think this is actually in the pedestrian precinct above Rodney Road near the junction with Larcom St, not Brandon St as marked on A to Z)
"We are a social enterprise training and employing long term unemployed. All equipment is tested and items suitable for reuse are diverted from landfill (distribution to voluntary sector organisations, small start up businesses and disadvantaged members of community). All old and broken equipment including CRT monitors are recycled in full compliance with EU WEEE regulations."