Thank you both. Yes I am gardening (or trying to) in Shetland! I have one plastic bin and two wooden compost bins, also courtesy of the local authority. Even the plastic one is not functioning well, it is in a more exposed windy site, so perhaps I should move it to get it warmer. I take your point about keeping out light. The wooden bins have a sort of quilt cover, but I think it keeps out the rain more than the light. I'll work on that one.
Re the perennial weeds - these are growing up from the soil underneath the compost bins. I dug and dug everything out before setting out the bins, but they seem to manage to still grow up through the rotting stuff. I am careful what I put in the bins given the problems I have on site with perennial weeds. I have put membrane on the bottom of one of the bins now and I'll see if this helps, but it presumably will stop the worms getting in! Can't have it all I suppose!