damp problem with concrete floor with no dpm

[trackside]

I have been having probls with mould and condensation in my ground floor flat and I have discovered that the damp is coming through the floor as I have drilled some holes in the floor and the damp meter readings are high in all the rooms and in the front bedroom the tiles under carpet are bowing and cracking and i have found out that there is no dpm fitted in the floor and a sand and waterproof mix was used when the flat was built in the 60,s and after so many years i think it is breaking down and i have to run de humidifiers in the house to keep the problem under control . What I need to know is what to do whether i need to replace floors in house or whether there is another way of fixing the problem.