Hi,

Is the render porous in any way? Any rain landing on a wall in that
situation (surrounded by trees and sheltered by a hill) is not going
to dry off quickly, and will soak into the render given the chance.

Something else to consider is that a wall has a high thermal mass so
will remain cold for some time after the heating has switched on,
especially if it is damp. Heating the house for short periods could
make the problem worse as it will allow moisture removed from
elsewhere in the house to condense on the walls before they have a
chance to warm up.

A better way might be to continiously heat the rooms with sufficient
background heat, leaving the doors partly open so the warm damp air
can find it's way out of the room. Or, use a dehumidifier.

Mould also tends to thrive where there is a lack of air movement, so
moving furniture away from outside walls will help. Even a few tube
heaters below problem areas will greatly help air circulation.

I'd expect the same house in an open situation would not suffer damp
problems, the developer probably used a standard design without
tailoring it to the surroundings. Your roof looks like it has some
moss on the top which indicates how damp the surrounding environment
is.

Looks like cavity wall insulation could be the way to go, it will make
the rooms easier and cheaper to heat too, but it might be worth
consulting an expert on damp to get their opinion.

Anyway sorry for rambling on, hope this helps in some way,
Pete