The wall is going mouldy because of moisture on the wall.
The moisture will either come from outside - a leaking gutter for instance so go out there when it's raining and have a look... or the moisture will come from condensation of the wet warm air in the house against a cold external wall - worse if a wardrobe or chest is against the wall.
Clean off the existing mould with a fungicide - let it dry and scrub it again.
Have a bedroom window open as often as possible, even a little bit - turn the heating down in the room, even a little bit - close kitchen and bathroom doors when cooking and bathing and open a window in those rooms to let any steam out.
Warm wet air and insufficient ventilation will allow some condensation against a cold outside wall and you may never stop it completely and double glazing and central heating do not help.
A dehumidifier might be a good start - mine was £160 with a 5 year warranty.
Good luck...
Peccavi
April 2009