Many thanks, ericmark. However, although I can see what you mean on the photo, it doesn't in fact have a circlip. I've tried turning the fitting but it won't budge, though I've not tried too hard in case I break it.
Probably a stupid question. I am trying to replace a light bulb (first time in this bathroom), but can't remove the cover (image of part of it attached). Does it unscrew, prise off, or what?