Wendy, I abdicated from recycling a couple years ago but may well go back to waste stuff soon!
It's all a question of building more recycling plants once a potential market for the product has been found, and then collecting the raw materials for the new recycling plant. If you get it wrong you get headlines about rubbish being exported not recycled (if the plant opens late), or recyclate used for low-value usage (eg glass pellets used as road ballast, if the local market isn't there). So it varies by borough, step by step.
Your council might give you a green bin anyway if you say you don't have one? There's only a few organisations collecting kitchen scraps, because early schemes had big teething problems, and depending on where you live it may cost a fortune for someone to collect it at sensible intervals. The places that do collect seem to be focusing on workplaces at the moment, so they can get lots of material from one place. I can recycle batteries, CDs, and mobile phones at work, as well as all plastics type 1-7 if I wanted to take them in!
My council collects all paper and card, cans, glass, plastic bottles and tetrapacks, in orange sacks, weekly on the same day as the rubbish. I have a compost bin but it's nearly full. The council will give me biodegradable bags or reusable bags for garden waste and then you phone and they collect, but so many people want to do this now that they've had no bags available for the last 2 months...
Still, better than the councils that decided the most economic solution was similar recycling bags, but tough enough that they and rubbish could be collected in the same vehicle, so they only needed one lot of trucks and drivers. At the recycling centre, an optical sensor diverted orange bags to recycling and the rest to landfill.
Worked a treat. Except the public saw the same truck collecting recyclable and non-recyclable waste, jumped to the conclusion that "it wasn't really being recycled", and stopped putting anything out for recycling. They had to get separate trucks in the end.