Does it have to be a new floor?

NO!

At uheat we have supplied thousand of underfloor heating systems for use in refurbishment projects. From the revamp of a small en-suite or cloakroom to a whole house renovation we have underfloor heating products specifically designed and manufactured to work on existing floor bases.  Super thin to ensure that the sometimes critical floor height is not raised too much, and products that will fit in areas from just half a square meter upwards, so No it doesn't have to be a new floor!