A house built in 1945 would have more then likely been constructed by mass concrete as the concrete block as we know today as far as I know was not being used for construction. The walls would not have been constructed as a cavity wall as we know but a single wall from mass concrete.
There could be a number of reasons for the dampness,
Rising damp from the ground as these walls had no dpc
Penetration of water due to damage to the external plasterwork
There could also be water getting in around the window sill
leaking pipe work under radiator,
External ground is higher on the outside then the internal floor level.
Condensation due to the warm internal air condensing on the cold walls.
I would recommend to purchase a hygrometer to check relative humidity levels inside the property.
There are a number of treatments available once diagnosis of the problem is made.
For example
electro osmotic dpc
external drainage,(French drain)
external insulation
dry lining internal wall
proper ventilation
pressure check on your heating system.
if you goole the above it should help to explain further.
Im no engineer so I would advise to get some expert to diagnose the problem and the remedy for same.
If the solution is not done properly you could still end up with damp and interstital condensation and mould issues.