At risk of the world's dullest thread derail:
This tells you what they take and various rule sets - as you intimate, a cynic may conclude that dumping it in the street is a whole lot less hassle
Reuse and recycling centres allow Lambeth residents to dispose of a wide range of reusable and recyclable items for free.
beta.lambeth.gov.uk
FYI - 9 times out of 10 they don't ask to see your bills, and they have always seemed quite relaxed if you miss your slot etc
Wandsworth smugglers way takes a much wider range of stuff (assuming you have a suitable ULEZ compliant transport option)
For Wandsworth an ANPR computer thing tells you to pull over if you have missed your booking, or didn't register the number plate etc, but a polite chat with the staff normally means they let you in. "it's a borrowed car", "I've lost my booking details " or similar