skylight condensation loose plaster

[Christhescott]

I have recently moved into a new flat which has a skylight in the hallway. The skylight is old cast iron with single glazing. The problem I have is the plaster surrounding the skylight has burst and is falling off in places, I think this is a condensation problem but i am not sure how to go about fixing it properly. I have uploaded some pictures and would appreciate any comments or thoughts anyone has.

thanks.
-Chris

//www.diynot.com/network/Christhescott/albums/

Edit to add my thoughts were to strip the lathe and plaster off where its affected and put mould resistant plasterboard in place and maybe cut a vent into the loft space.