Hi fidaleo It’s not clear what your images are showing however if the concrete blocks are exposed on the outside you could try cladding the outside wall above ground level. Internal rendering will not be effective in the longer term. Regards S
The external wall has soil pushed up against it (next doors garden) so access to render the external wall isn't possible. I'm thinking rendering the external wall which is showing no signs of damp will only make the problem worse as run off will drop into the soil and produce even more moisture at the lower level brickwork.
The 3 pics show 2 internal pics of the wall in question and the side of the external wall. You should be able to see a clear demarcation to where it is dry and damp in the brick work. This matches the level of soil on the external wall.
So anything internal isnt going to help...
1. render upper level of external wall which is showing no signs of damp 2. dig up next doors garden down to the base level of the outbuilding and render
I'm not sure option 2 is going to fly with next door as she has a full garden in the flower bed,
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