Check out http://www.freecycle.org/ (it a pun on recycle, not bicycle...)
After bugging one of our local councillors, the every friendly and helpful Andrew Milton, we discovered Lewisham Council has a rather pathetic setup for dealing with old computer equipment.
However, the council did helpfully suggest the following:
The Council does not currently collect computers for recycling or disposal purposes. However, there a number of recycling schemes that assist residents, businesses and organisations recycle waste electrical and electronic equipment.
Some organisations that buy or accept IT related equipment include:
Other organisations that accept ICT equipment include:
Technowaste Ltd Caxton House Harvey Road Burnt Mills Ind Est Basildon Essex SS13 1QJ Tel: 0126 872 8512
and
Reco-Vie (Recycling) Dean House Farm Church Lane Newdigate Surrey RH5 5DL Tel: 0130 663 2777
Other sources also suggest:
Finally, via our good local councillor, we also came across this:
Emmaus Communities offer homeless men and women a home, work and the chance to rebuild their self-respect in a supportive, community environment.
They have shops across the country, including one in Greenwich. Your local branch can collect your unwanted furniture and small electric appliances and resell them.
226 Elmley Street Plumstead London SE18 7NN Tel: 020 8854 3426
Alternatively I think the British Heart Foundation on Old Kent Road also take electrical goods.