I've seen a number of topics related to damp stains on chimney breasts and on the ceiling above the chimney breasts. I have had this problem and seem to have chanced upon a solution.
I have an early Victorian cottage, two up/two down with a pitched roof and dormer windows. I had tarry stains showing through the plaster on the chimney breast in one bedroom. 10 years ago, to guard against any smoke leakage from the fire below I had the chimney relined with thermocrete, a fireproof concrete and afterwards I replastered the breast. Unfortunately this did not stop the stains coming through...I rather expected this because the tarry salts continue to work their way through unless all the chimney brick is completely replaced. The stains gradually get less in time.
Dampness all over the chimney breast in the bedroom and in the ceiling just above it has been a real problem though in recent years. Droplets of water could be seen on the ceiling right near the chimney and the chimney breast was slimey to touch with some run-down of condensation....enough to cause some dampness in the ceiling below. There has been no mildew, presumably due to the acidic salty deposits in the plaster coming from inside the chimney brick. It was not clear whether the damp was surface condensation or coming from within the chimney through the plaster. When it was raining, I poked some holes in the damaged plaster in the ceiling near the chimney breast to see if there was any water leaking down, thinking there might be a leak in the flashing. I was surprised to find nothing but dry dusty material above the ceiling plaster near the chimney....nothing soggy at all. The joists felt a little damp.
I towel-dried the chimney breast and ceiling as usual.
Anyhow, like magic, the next day the condensation had gone and the chimney breast was dry! It has stayed dry for several days despite continual rainy weather. I can only assume that ventilation was badly needed in the roof space. The roof space above the bedroom has never had any access like a trap door. When I repair the plaster, I intend to fit a small ventilation grill in the ceiling by the chimney breast. I recommend this solution to anybody with similar problems. So rather than ventilate the chimney flue itself(If your chimney is not in use) try ventilating the roof space. This may be contrary to logic. The idea in modern building is to prevent any warm moist air from entering the roof space to stop condensation on cold roof timbers above insulation. However, if the source of the damp is from elsewhere, such as condensation on cold chimney brick or penetration of damp through the flue(or many other possibilities) with no proper ventilation of the roof space this could be the source of the problem.