Morrissey, good evening.
Several issues, all possibly linked.
1/. From the sheer volume of moss, there is a really good going leak from either the down pipe or the gutter, indeed the gutter may??? be blocked at the entry to the down pipe [ a tennis ball does this job very, very well?? ] blame the kids?
2/. Yes the isolated damp staining internally is dot and dab, but why? do you know if the cavity of the external wall has had retro-filled insulation installed?
3/. A trip out during a rain storm with an umbrella, should locate the leak?? As an aside there is visual evidence of long term water staining on the outside of the plastic rain water down pipe??
Possible remedies.
A/. Find and fix the leak.
B/. Rid the external wall of the moss, use a moss killer and a soft brush later, several applications of moss killer may be needed??
C/. Once the source of the leak is rectified externally leave the internals for a wee while see what happens. to assist beg, borrow or hire a medium sized De-Humidifier and let it run, await results and see what you are left with?
My stock in trade retort is address the leak and let the damage mature internally?
Ken.