Refuse collection is a statutory requirement and residential properties already pay for the service as part of the Council Tax.
I guess what people are paying for is some sort of additional service to that of domestic provision?
Domestic waste collected ultimately goes to landfill, where there is a tax (landfill tax appropriately enough) levied on every tonne deposited there. The idea behind the tax is to get local authorities to concentrate on minimising domestic waste by means of increasing recycling collection - and thus reducing the tonnage going to landfill (and having to pat the tax on it).
If the reason you have a 'green bin' is to recycle normal household waste - such as paper and glass for instance, then I can't understand why you are being charged for the service?
If the council specifies a certain means of collection - such as a bin service - I would have thought they would provide the bins free of charge.
I'm sure there must be a reasonable explanation for the charge from the council but I have no idea what it is from what you have said?
Maybe the explanation is on your local council's website?