The wall in question is the outer wall of a second floor flat that I let. Unlike most scenarios described in these forums, The mould is very fine and grey, rather than black. More liike a 'paint effect'; it brushes off, and I have washed over it with a fungicide.
It is most noticeable under two windows, at its worst in a dark secluded corner of the same wall. The wall does not feel particularly damp, and the mould is not charecteristic of the black, blistering fungus that one sees when water is leaking in from outside. The pointing seems reasonably good , and the gutters above were replaced recently. The plaster/ paintwork is perfectly sound and not cracking away at all. There is no musty smell, or any charecteristics of dry rot. The flat below has no similar problem.
I suggested to the lodger that the cause was excess condensation, and might be cured by more ventilation. The windows are D/G units , and condensation does manifest itself on the kitchen window. The heating is by storage heaters, on a low setting.
I added that the flat, being on the second floor of an older property, has no 'outside door' to speak of, and no draughts or throughput of air, so one has to make an effort to change the air in the flat.
Am I right in thinking this?