corner at the bottom or at the top? Are there radiators nearby?
is one of the damp rooms the kitchen? has it got a solid floor? if wooden floors, how may airbricks have you got, and are any of them buried or blocked with cobwebs and dirt? Do you know where the water main comes in, and is it iron, lead or plastic? (iron water mains tend to rust through at the elbows after about 50 years).
1930's houses will have underground drains made of glazed clay (earthenware) with iron above ground. Both of these will crack if there is any movement in the ground, as happens seasonally with clay soils, and in cities during the 1939/45 Unpleasantness due to bomb damage.
poke around round the drains and see if the soil seems unusually damp or smells. If it is concreted knock on it and see if it sounds hollow or looks like it has been repaired (leaks wash away the soil and leave a gap)
if there are downpipes near the wet patches, look at them during heavy rain and see if water is spilling from the gutters, hoppers or joints (this will happen if there is e.g. a leaf blockage) or if iron pipes are cracked or rusted.
250mm walls are solid brick (no cavity) being 9 inches plus an inch of plaster. Cavity walls are about 325mm thick. Cavity walls are damp resistant if they are properly built and the cavity does not have rubble and dropped mortar down it.