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Reading that, the first quick & easy fix would be to remove the concrete plinth up that is bridging the damp proof course, and to stick a French drain in there, and strip the render back above the DPC. Then strip the plaster back to brick, and leave it over winter to see if it fixes the problem.
Someone from mybuilder.com should be able to do that pretty easil in a day or two.
I reckon that mould around cold water pipes is likely due to a small leak, and should be easily fixed (it could be condensation, I suppose).
Chemical injections are woowoo, if you ask me - they appear to be a default solution to all things and anything damp related.
What sort of wall is it? Stretcher bonded (likely a cavity wall, and post-1920s-ish) or stretcher & header bonded (pre-1920s-ish and a solid wall)
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It is definitely pre 1920's, 1907 if I remember correctly. Walls are either English bond or English cross bond (will have to check the neighbours' brick pattern tomorrow to confirm) with one, or several layers, of render accumulated over time... I think I will follow your advice and get a good builder to have a go at the plinths and repair render. I will also will to have a good read about DPC... I must confess I have no f... idea of DPCs
Seeing the survey it seems that, regardless of the damp proofing, we would still have to get a builder to check under the decking and retouch the render. So we wonder if the damp proofing is still worth it. They quoted £2000 for the whole chemical treatment, plasterwork and súper fan (£300 fan!) installation. Quite a lot of reading 📖 but I would appreciate a second opinion