Some of the big garden centre chains that used to offer a pot recycling facility have now withdrawn it because of the difficulty in separating out all the different plastics, such as polyethylene , polypropylene, polyvinyl chloride (PVC) as they can't all be mixed together. Some can't be recycled at all. The bulk plastic needs to be sorted at a specialist recycling plant. PVC sinks, the others float so have to be sorted by hand. I have seen one of these plants, with a big water bath and conveyor belt where plastics are sorted. What a job!!
I suspect that a lot of it is shipped to the Middle / Far East for recycling, and I fear that some of it is then landfilled, but I can't be sure.
At home I try to separate out my plastics into those that can and can't be recycled. OH just told me off for putting plastic packaging from bacon in the recycle bin. It should go in the black landfill bin!