Update, but no resolution yet
I've spoken to the neighbour and been inside on his side. They have exposed stone walling in the area in question. The mortar is also clearly damp up to the same height. It would seem that it was a known issue. Adjacent, they have a small kitchenette area which has been built away from the wall. Presumably, to let everywhere breathe. Unfortunately I don't have any direct pictures. The ones below are taken from Rightmove when he bought it in 2018.
My next question is, how do I mask the damp on my side?
The neighbour, a builder, suggested that I batten it out. Leaving an air-gap top and bottom to allow it to breathe.
If I was to do this then I was going to use foil-backed board but, would any moisture evaporating from the wall possibly condense on the back and run down the back rotting the carpet below?
Alternatively, could I paint over the plaster with SBR, sealing it all in and then paint over with emulsion?
I know you'll say to "do it properly, do it once" etc but, it's a rental property. I realise that it may need painting again every couple of years. I really don't want to be chopping it all back to the stonework and injecting dpc etc.
Another thought, as it appears that next door have done, could be to put the radiator on the damp wall. This will at least keep it warm and all at bay. In the winter at least.