Hmmm.
recycle-more.co.uk doesn't give information in a useful form for round here, nor is it complete. I can think of three small electrical appliance recycling bins within five minutes of here, each as part of bigger recycling banks. Two simply aren't shown on the map or listed, while the other is shown as being for batteries and waste electronics while it's actually for paper, plastics, the works ... And the only dump shown is for another borough.
On the plus side, it does seem to tell me most of the places I can recycle batteries.