Replacing concrete slab with suspended timber floor

[alexc1979]

My Victorian sandstone mid-terrace (no cellar) has two floor sections (front and back of main room) on the ground floor. One half is floored in traditional suspended timber but the other has a cracked, uneven concrete slab. There is also a 2m wide section of rising damp in the wall in the concrete-floored half.

Since I would like a nice even floor to board out in laminate or similar, and I am also considering water underfloor heating (there is currently no central heating), the question is whether I should consider breaking up the concrete floor. This would clearly be disruptive and messy, but I also suspect it would deal with the rising damp if properly ventilated.

I know that it was once popular to strip out rotten suspended timber flooring to replace with concrete, which could be what happened here, but has anyone experience of going the other way and taking the floor back to its 'proper' state? Is it worth doing and is there any good advice?