You need a combination of heat and ventillation to reduce condensation. Th heat will allow more moisture to be held in the air and the ventillation will carry it outside.
The mould will need to be killed off with a proper antifungal treatment or it will persist. The spores are not good for you.
You will need to make sure the outside of the walls are not letting dampness in. This can be from the ground level being above the DPC, leaking gutters, driving rain, damaged pointing, frost damaged or perished brickwork, etc.
If the outside is dry then it should be an internal problem, condensation or leaking pipe.
Insulating the walls on the outside will help prevent interstertial by keeping the wall warmer while insulatin the inside will need to be done with a vapour barrier to prevent moisture condensing inside a colder wall.
One way of finding out if the moisture is from the room or the wall is this.
Using a glass bowl, seal the rim with putty and stick it to the wall. Leave it over night and see where the condensation is. If it is wet on the inside of the bowl then the moisture is coming through the wall. If it is wet on the outside of the bowl then it is condensation from the room.
Use plenty of ventillation, either natural or mechanical whenever you are cooking or boiling water, doing washin up, or anything else that puts moisture into the air.