I agree with Head Nun. My experience is very similar and has been so for the 25 years I've lived in London.
They got a lot worse after the Tour de France came here though. And then the Olympics.
You can request for them to come and collect your full bins again
https://forms.southwark.gov.uk/ShowForm.asp?fm_fid=1879
They usually come on whatever day your rubbish/recycling collection day is. If you aren't going to be in, leave them somewhere that they can find it. If you don't need replacements, just leave a note on the full ones that a replacement isn't needed.
They usually come quite early, so it's better to leave them outside if you can.
Cyclists certainly do have a bit of a perception problem at the moment and when I cycle I see a lot of examples of arrogance and ignorance that gives all cyclists a bad name - it does seem that many cyclists have caught the entitlement bug many drivers seem to have.