Fair enough. If the problem involves the whole house, there are obviously potential energy/cost issues involved with continuously extracting the heated air from the whole house (unless one has some fancy heat-recovery system!).
Which would be a sledgehammer...
It would seem sensible to start by eliminating/reducing major avoidable sources of humidity (such as drying of washing), including specific extraction of above-cooker air etc., and maybe even to consider the use of dehumidifiers.
Spot on! Extract the over-moist air, directly at source, put rules in place, no need for a dehumidifier.
Ironically, in the days when many were installing central heating for the first time, one of the 'complaints' was about 'dry air', which lead in some cases to deliberate measures to 'humidify' the air!
We had both issues - too dry air, yet in some areas, it was still humid enough to grow mould - plus high heating bills, from running the temperatures higher, trying to combat the mould.
Now our bills are much lower, and we have no mould. Insulated, DG'ed, added local extraction at moisture sources.
