If you have a leaking supply pipe under the floor then (unless it is near-new and there is an easily corrected fault) it is usual to lay a new one.
It's very common in old houses.
You didn't say if it's a suspended wooden floor or a solid concrete one. Of course it is much easier to lift a wooden one that has a space underneath.
The new pipe does not have to follow the same route as the old one. Often it can be less disruptive to dig a trench at the side of the house.
If you're laying a new supply pipe, I strongly recommend doing it in a largerer size of plastic, at least 25mm but preferably 32mm. The cost of materials is little more, and the effort of digging the trench is the same. A larger pipe (all the way to the watermain under the pavement) will give better flow and enable you to get the best from a modern unvented cylinder or large combi, making it possible to have powerful showers and not get the water running cold and hot when someone turns on another tap. Make sure you specify full-bore stopcocks and service valves (the larger ones are more expensive and if the plumber "forgets" it is a hundred times more work to dig up the pipe later than if they had been done in the first place).
Your water company will have to inspect the new pipe before the trench is filled in, to verify it is correctly laid. Or if you employ one of their approved plumbers they can certify it. They are usually more expensive. No great skill is required to dig a trench and connect a pipe. A builder or labourer will often do the heavy spadework, or a householder who likes gardening.
Contact your water co at once. Maybe they offer a subsidy for replacing old pipes, especially if lead. They must test the water before you start work.