Damp/wet high up internal wall on corner of house

[britishboy7]

In our 1930’s semi detached, the staircase is in the un-ajoined front corner of the house. The stairs follow the corner around so there’s a high void right in the corner that is approx 4m high. There are signs of wet/damp on the plaster (was done about 4 years ago) and it’s starting to go black in a few places. Majority of it wipes off with a cloth. The hallway isn’t the warmest of rooms even with the radiator on - it’s open so all heat I’m guessing heads up the staircase to the landing.

It’s only there in the winter months.

Have checked the gutter above, and in the loft so I’m assuming it’s due to temperature variation in that particular corner.
Any ideas where to start please?

 

[foxhole]

External pics?