I am looking for clues
You say you have them sitting in trays on top of damp compost in an unheated greenhouse.
Are they new tubers or tubers you have saved through the winter?
If new! then it might be too cold for them and it all depends on how damp is 'damp'! If they are too damp this can make things cooler still, I have an expression to describe this and that is they want to be the damp side of dry if that makes sense!
If they are saved tubers how did you keep them through the winter?
They've been there for a month and I thought they'd have shooted by now.
I would have thought so too!
There are some pictures here on how I do it;