Have chimney stack that has had new lead flashing and repointing, it is a double chimney, one used as coal fire which we hardly use, the other not sure, roofer said when repointing it had been sealed so he put a vent in to create air flow, it seemed to help dry a small brown damp patch that we had in first floor bedroom, but now seems to have created another, slightly lower down still on 1st floor. Must say house was a bungalow, but bedrooms put into roof space, house built about 1932. Had roofer back but he said it might need ventilating lower down and said we should put a vent in bedroom towards skirting, by drilling 6 holes into chimney breast and covering with a vent, is this right advice.
Any blocked chimney would need a room vent. Worth trying. You could fit a plastic vent over the new opening that would be cut out. Something like this: http://www.screwfix.com/p/map-vent-adjustable-vent-white-76-x-229mm/9414d
Assuming there's no other external defects eg guttering issues, wall pointing issues etc Then... Hack off the plaster. treat brick with salt stabiliser. 2 coat brick with sand and cement render after scud coat. skim. paint. Those stains are from hygroscopic salts from the brick. burning in chimneys is known to cause such problems.