The bay window ceiling is showing signs of mould spots about to burst through the wallpaper covering. The bay window roof is flat, and tends to be the coldest part of the room in winter (not been able to find the source of the draft).
If it was condensation related though, I would think that the mould would be growing on the surface of the wallpaper, rather than "beneath" it.
This leads me to think that the problem is more likely the roof needs looking at.
The roof looks like it is lead but has been painted over, and the paint is flaking off. In think over the years bits of debris from the main roof falls onto it, and that might have punctured the covering here and there.
I am considering putting a few coats of bitumen paint over it to stop any water possible ingress.
Any advice on what to do on the outside and inside would be much appreciated.
I'd like to avoid having to do any redecoration internally.