so it may well be an iron pipe that has rusted through. Possibly at the elbow where it turns upward to come through the floor. If so I would hesitate to spend time having it repaired because all the rest of the pipe will be the same age and no reason why only one bit of it should be rusty. So I would run a new plastic pipe. It does not have to be in the same route as the old one.
To see if it is the supply pipe, get someone to turn the stopcock on the water meter, or buried in the garden next to where the front gate used to be, on and off. If you are near the leak you will realise that the hiss of the leak stops and starts, even though you were not aware of the noise when it was constant.
If you are on a water meter, notify your water supplier of the leak, they may give a rebate for the wasted water.
If the leak is really under the conservatory, it might not have made the house itself very wet.
Look on the bright side, if you have a new, larger, plastic pipe run, you will get better water flow and can improve your plumbing.
Digging the trench and laying the pipe might take a couple of days, the dehumidifiers used might be the size of washing machines on casters and will suck in the damp air and blow out warm dry air. They are a bit noisy. They will warm the house and the insurance co will pay for the electricity. You shut the door on them as they work best in a closed room.
A house of that age should have effective DPCs in the walls, so the damp should not have got into the fabric of the house. If you need a new floor, it will incorporate a DPM so it does not matter if the ground underneath is damp.