In reply to Removed User:
I'd agree with the above. Are the walls very damp too?
Are you able to improve the drainage around the house?
If the ceiling is quite high and you can afford to lose a little height. You could put in a damp proof membrane (posh word for thick plastic sheet), then add a thinner layer of concrete on top.
The problem is if the walls are single skin and are very damp, what you call damp is just them breathing the moisture from outside. Better to stop from the outside, not in.
If you can't do any of the above, get some thin bits of granite (non porous) and sit boards on them, to put you stuff on top off. Don't cover the whole floor, leave space for the air.