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This caught my eye because we had this problem. You really need to address the source of the damp. If you have render bridging the damp proof course outside -- which is surprisingly common and very stupid -- it's an easy fix. We got a building surveyor to look and he figured it out -- he charged a bit but it saved the chemical damp proof treatment which doesn't address the problem.
@TW gives pretty good advice to start with.
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.
This is what we did 15+ years ago and it has been fine ever since.
edit: also check for cracked or blocked down pipes and drains in the vicinity.
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