Hi Raymond,
I found the following in one of my books... a short term solution is to scrub it off and paint the area with neat bleach. This usually doesn't spoil the paint, but do a test patch first! From then on, put a dash of bleach in the water whenever the windows are washed...wearing gloves of course!
I did this in my bathroom at previous house and it worked a treat! Also, I tried mixing it with PVA glue (very cheap) and applying it with an old brush, which made the bleach dry onto the surface.... painting bleach onto it every so often.
Mould spores are in the air so the only long-term solution, I'm afraid, is to get rid of the damp conditions.
Good luck!