This sounds like mould caused by dampness. Try putting a dish of salt in your window bottom or buy some absorbing crystals (wilcos I think). They do work better.Try to air the room well by opening a window.
Thanks for your answers!
I've just moved into a bungalow, and there were several spiders, craneflies and beetles (still trying to get rid of them!), so that must be it as there isn't any dampness or mould.