Mildew on en-suite extrenal wall

My house is approx 14 years old. It is brick and block construction and insulated with what looks like polystyrene balls.

The en-suite is on an exposed south facing external wall. It has a single window approx. 900h x 500w and a 120mm fan (replaced about a year ago ). The room it self is about 1800 x 2400.

The window tends to be left open most of the time we are in the house and the fan is used when showering and is on a timer for about 10 minutes after switching off.

On the wall above the window and the ceiling above that, in a patch that extends about 500mm into the room, there has always been mildew.

I am wondering if we are drawing cold air in the whole time we have the window open and if it would be better to leave this shut and just use the fan.

Does anyone have any other ideas ?

Also are there any safe smoke testers that could be used to check the fan is working OK ?

To check whether your fan is working OK, get a piece of kitchen towel and hold it up to the fan. If the towel sticks to the grille, the fan is sucking air out fine. If it doesn't, then look at the grille and see if it's blocked with fluff. If it is, then you will need to remove the grille and clean it off.

Re the mildew itself, have you tried using this to remove the mildew: http://www.polycell.co.uk/products/polycell_mould_killer.html

Reducing ventilation will have an adverse effect, increase fan timer to max, it may not be effective enough so consider a more powerful model or a second unit.[Assumes you have checked condition of existing fan as Nick mentions].