Damp around upstairs chimney - stone saturated rather than a leak?

In the event that you can’t find any evidence of water or moisture penetration then another damp problem inherent to chimneys and the areas around chimneys is the presence of hygroscopic salts (sometimes known as Chimney Salts). These are usually deposited as a result of burning fuels. As we all know fuels generally come from the ground (e.g. coal, wood etc….). During the time that these materials spend in the ground they can absorb salt minerals, sulphates, nitrates etc…. When the materials are burnt these salts and minerals are released and settle on the inside of the chimney. Over a period of years these salts can then penetrate through the brick or block-work of your chimney breast and onto your inner walls. The salts themselves are hygroscopic (moisture attracting) and when present on your chimney area they attract the moisture within a room space and can create damp patches on your chimney breast. Any staining caused on these patches, in most cases, is the result of soot and other particles that have also managed to creep through the wall over a period of years.

I would agree that salts seem to be the issue. The cure is to take off the plaster (if it is plastered) and render using a salt inhibitor. ( sand and cement render) Also, is the flue in use? or if it is capped off, then it should be vented with an air brick in the stack and chimmney breast.