OK
shovel out the rubble (you can get rubble sacks at places like Wickes)
some council tips will take them. Mine charges £3 per bag, I think
Shovelling out the rubble should reduce the damp somewhat. You may notice the colour of the bricks and concrete get lighter as they dry. Take weekly photos so you can see if there is a change. If you can see a wet tidemark, draw round it with chalk so you can see if it recedes or grows. If you have a table fan or room fan (not a fan heater) you can position it to blow onto the damp bricks to increase evaporation.
if the base of the hearth is flat smooth concrete, lay a piece of clear plastic on it, and tape it down tightly. If water droplets form underneath, damp is coming from the floor.
Once it is swept clean you will probably see marks if rain is running down from above.
A 1930's house will have a dpc in the walls, but nothing under the hearth. Typically, after the brickwork for the chimneybreast had been built, it was filled with assorted builders rubble and a concrete slab poured on top.
rubble is very absorbent of damp.
once the fireplace is out of use, there is nothing to keep it warm, dry and ventilated.
Usually this can be corrected by breaking the slab and digging out the rubble, so the brickwork is exposed to the air and moisture can evaporate off the bricks. It may be two feet or more deep.
We have had some other similar cases arise here.