It's a small building job. First thing is to identify the source of water. It might be a leaking pipe or drain. It looks to me worse and more local than damp caused by blocked airbricks.
Having cured the damp, the subfloor void needs to be ventilated to dry out. This needs airflow, not heat.
Quite likely you will then need to dig out the earth and lay some concrete pads so the new joists can be supported on bricks, with a piece of DPC under the joists.
All that is easy for a competent builder, and not a big job. But you need an established and experienced reputable person. Try to get personal recommendations. For some reason parish magazines are often good sources of reputable local tradesmen. Even an old chap who has retired from heavy work could do it.
Curing the damp is the most important thing. Do not believe anyone who tells you it can be done with magic beans, or silicone fluid, or ceramic sticks, or special plaster, or by covering it up so you can't see it. Damp is water and it does not spontaneously occur. It always comes from somewhere.
Some people will tell you to cure damp by pouring concrete over the wet earth. This usually covers up, but does not repair, the source of water, so it later appears in the walls and other rooms, and is a hundred time harder to rectify since the concrete has to be dug out to get to it.