This has been a problem for a while, but I have avoided thinking about it because the room is mostly unused. This is a photo of the damp on the chimney breast in the attic. Apologies that the photo isn't as clear as I wanted because of the lighting. It doesn't feel wet, though it does feel very cold. The damp is not in the bedroom or living room below. This room isn't used regularly, so I don't think there is much humidity, but there is an occasionally used en suite shower on the other side of the wall.
I have also attached a photo of the outside chimney - it seems to have caps on the tops.
I think it seems insurmountable so I've put it off, but I'd love to be able to sort it. Any advice much appreciated!