Mould will only grow when relative humidity is above 60%. However. once its in the house, its hard to stop. Contrary to many posts I've seen, bleach DOES NOT kill mould. You can clean mould away with water but the only thing I found that actually kills the spores and hyphae is something called Teflex. It's available in Ireland and really did the trick in our utility room.
Treat the mould and then find a way to reduce moisture build up. If all else fails, look for a mould remediation company.