Hello Velvetee and others!
A dehumidifier (the electrical kind) is definitely the best thing to do!
I've had one for years in my small flat in Paris, it uses as little energy as a fridge (so you can save on the heating!), and isn't much more noisy. With it, I managed to keep the humidity level below 70% at all times (even on rainy days in the winter when I had to dry my washing inside); without, the humidity level shots up to 90%.
I'm currently renting (houseshares) and in my current house, there is a problem of mould, especially in the loo, the bathroom, and my room, which is very small. It is ventilated (the cheap PVC window lets in a draught even when it's closed, and when it rains, I have water on my window sill). I open the window every evening to renew the air, but it has to remain closed during the day (risk of burglaries) and at night (cold) and I do need to breathe, and the air you breathe out contains water vapour...
I can't have a humidifier (not enough room), but I do use calcium chloride, and Dettol mildew remover (beware, it contains bleach, and I've just damaged a pair of trousers while doing my Sunday room-cleaning). I had never had mould in Paris, even before I had had a dehumidifier, but then my building was very upscale, whereas the house where I'm renting now is a Victorian terrace, cheaply built.
Best thing to do would be to pull the house down and rebuild it. I know quite a lot of people who rent, and for humidity and mould, the worst offenders are basement flats: you don't stand with your back to the wall, because you can hear the mould whispering 'come on, guys, let's get him!'.