This comes up a lot Barry. Especially in this country, at this time of year.
I've said it before. De-humidifiers only address the symptoms: not the causes.
237sj's surveyor is right. Heating and ventilation.
I imagine the mould is developing at the top of the wall, in the angle between the wall and the ceiling.
It's rather a shame that most people set their heating to go off at night, at precisely the time that it's needed most. The only way to avoid having the heating on is to apply extra insulation to the wall surface and/or increase ventilation.
At the very least... add ventilation. Trickle vents in the windows are effective to combat condensation on glass, and do help with the walls.
Start with a simple method. Add a vent /grill fitted into the ceiling at any point where the mould is developing. You may only need a couple of them. A 9"x6" grill will do.
The pukka way is to duct from the vent, through the roofspace, to the outside. For starters, just let it vent into the roofspace without ducting. The space should be well ventilated anyway in a well-designed roof. It's a start.
I've sorted this before many times. If mould is all over an external wall, then I've just added modern foam insulation board (finished with plasterboard etc.) That, with ceiling ventilation does the job, even without added heating. It's not guaranteed. It really does need the air temperature in the room to be raised above the dew-point.
So easy in a new-build. Much more difficult in any property built in the last 100 years.
Houses older than that are often so leaky, they ventilate themselves.
I do wish I could offer a magic solution Barry, but it really is a matter of trial and error.
Either heat, or "real" ventilation. Preferably both.