Condensation
Unless there is a specific cause for dampness such as leaking roof, walls, gutters, drains, water pipes or rising damp, mould is more often caused by condensation - air born water vapour.
Condensation in turn is sometimes caused by inadequacies in the building construction, such as poor ventilation, insulation and inadequate heating systems (an older house, of solid wall construction, is unlikely to accomodate cavity insulation), but often it's caused mostly by the lifestyle of the occupants. Too much steam generated within the house from cooking and washing, coupled with too little heating and ventilation.
The longer a house has been subjected to this, the more the dampness and mould takes a hold in the fabric of the building and the quicker these symptoms re-appear when conditions again precipitate it.
In practice properties are too often left all day with little or no heating. When evening comes the occupants return for just a few hours to literally blast the building with heat and moisture from cooking, washing, breathing etc whilst providing little ventilation for all of this moisture. The walls are cold from lack of heating during the day, so all the moist air which rises to the top of the house (bedrooms in particular) which are the coldest, condenses out, causing mould to form on wall paper and on clothes in wardrobes and behind furniture.
The tell tale signs are condensation on windows and sills, mouldy curtains and blinds, black patches on the wall paper in the top corners and a musty smell in the rooms. The solution is to keep the house thoroughly dried out and warm by providing adequate heating, this can take some days or even weeks to do. Once the house is warm, the key is to make sure it is heated little and often to keep a constant temperature throughout.
Keep the house well ventilated, especially vent-out steam production from the room, where it's made instead of letting it spread throughout the house i.e. from showers and tumble driers. Do not dry clothes on radiators inside the property. Keep each room in the house warm, where possible.