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Barnet recently switched to charging to take away garden waste. If you haven't got the magic sticker the bin men will not take it away. Garden waste is emptied once a fortnight and you can have as many green bins as you want to pay for.
I could bag up garden waste and put it in my landfill bin as there is always lots of space in that but it feels wrong. At least my garden waste is turned into compost someone uses this way.
At the moment I have two 240l garden waste bins and ~600l of compost bin in the garden (those have been active since last autumn and are full of not nearly rotted down stuff, probably too many leaves).
jellybaby-
I'm happy that i work as a binman for my local council, there is almost no supervision. In my city bins aren't being registered at all, people just call in to say they lost theirs and they get a new one, free of charge. Obviously some people abuse this, so I'm actually drafting up a bin consensus program with colleagues.
Föhn
Have you tried filling your regular bin with the organic waste and asking the binman if they would mind emptying this one as well on collection day? Some of my colleagues have no problem doing this, others refuse.