Also ........... I guess that a 1930s house has been re-roofed at some time. Quite possibly it was done with old type non-breathable felt. If so, your problem (apart from the poor insulation at the perimeters) is a lack of roof ventilation.
Any roofer can fit slate vents for you to give a decent crossflow.
The way to check is to have a look at the underside of the slates. If you see tar type felt, then it's possibly unventilated. If you can see the underside of the slates, then you are ventilated.......... and I'm wrong about the lack of ventilaton. ;o)