Lambeth borough used to collect large items of household waste for free, up to a maximum of 4 times a year, if memory serves. The current system in Lewisham of charging for collections doesn't discourage fly-tipping by the feckless, but as Londondrz says, it is only a 10 minute drive to the tip on a Saturday morning*.

Some time ago I had an argument in the street with someone dumping rubbish - their view was that I shouldn't worry because the council would just come along and pick it up!

(*I actually find it oddly enjoyable to see what's being thrown away at the tip. I admit it, I have a problem).