I have never heard of something like this before, but I am aware of houses built on slopes with rooms on different levels having voids. These are not intended as living space and often are not tall enough to be used as anything more than storage although an uncle of a friend of mine built a model railway in one.

If the house had previous owners I would suspect one tried to create an extra room but gave up once his excavations started to fill with water and you may be right that the water is the source of the damp conditions encouraging mould. I would fill up the holes with gravel put a blinding layer of sand on top on top of which I would cover the whole area with a damp proof membrane finishing of with a 100mm layer of concrete. That should seal the dampness but you still need to ensure adequate ventilation.

Richard