I bet it’s bathroom damp rather than damp from the roof above.

Lots of old people have an unshakable belief that you need to keep a window open in the bathroom to get rid of steam. It’s actually the worst thing you can do as air from outside chills surfaces which causes condensation which causes this problem.

My mother in law contributes further to the same bathroom problem by always having clothes soaking in a bowl and drying her washing on a rack also in the same chilled room.

Here’s what you do:
Wash off the mould with a mould remover.
Paint over the marks with a stain blocking paint.
Stop the issue happening again by keeping the window shut, keeping the room heated, then installing a good extractor fan and ensuring that the roof space above is well insulated.

Thanks so much - that seems achievable for me to do. You are spot on that was an old person in the house previously as indicated by the decor.