I met the father and daughter team, Dave and Tracey, and learned about their special business a while back at the Table View Urban Farmer's gathering. The essence of their business is that for a small fee they drop off bags and pick them up again, and then sort your waste and bring it to larger recycling companies. They do paper, cardboard, glass, metal, plastics and Tetra Pak (foil lined paper cardboard containers for juice and milk). Contact them at email@example.com or at 0834444123, or 0837748291.
They do not do cling wrap, disposable nappies, chemicals and a number of other odd elements of waste. If you use their services in addition to a home worm bin for your organic waste, and find out about recycling/donating clothes, you will come incredibly close to the No bin waste ideal. This is why they are being granted the Nobin Prize for May. They take you much more than half way there.