In principle all concrete floors should include a damp proof membrane across the whole floor area and this should be linked to the damp proof courses in the surrounding walls to provide continuity of protection against ground moisture.
It follows that any breaks in the membrane will lead to dampness of one degree or another within the floor area. Because the source of failure is often so difficult to pinpoint, you could be looking at having to renew the floor in its entirety.
One alternative that may be feasible is to apply an epoxy resin coating across the floor to seal it against damp. Two coats are usually required with say 6 hours between, so it can be done in a day. But you need to be able to get at the whole floor area up to the surrounding walls so if it's a kitchen, all the units will have to come out. Surface preparation prior to application will be crucial but even so it will be less disruptive than taking up and renewing the floor.
Not a DIY job though.
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