We thought the Asbestos Palace was cursed with damp, but it mostly seems to have been a leaky dishwasher that had spent who knows how long distributing water along the bottom of the kitchen wall. There was general dampness behind appliances that was probably just moisture condensing on cold exterior walls. The bathroom didn't have an extractor fan and had similar problems.
Anyway, we bought a dehumidifier and ran that over winter to dry out the kitchen and that seems to have done the trick. We run that when we dry clothes in the house and keep a few windows on the latch even in winter (judging by the effort to open them and the general mouldiness of the windows, they'd not been opened for a while). In the refurbishment works we had decent extractor fans fitted in the kitchen and bathroom, and had the side alley path re-paved and some DPM paint along the render were water was along the side of the house and we had the pipework and spillway replaced to ensure that liquid didn't gather.
All seems to be good now, the hygrometers read between 35-60% – it's amazing how quickly it can rise when cooking etc. We occasionally have to wipe condensation from the upstairs window corners in winter, but that's about it and we dry all the washing indoors.