Underfloor heating comes in two forms. Electric systems use heating cables or mats embedded in or beneath the floor finish. Wet systems circulate warm water through pipes laid in the screed. Both deliver gentle, even warmth from the floor surface upward, and once installed they are completely invisible - a real advantage in a listed interior where wall-mounted heaters or overhead units would alter the character of the space.
The catch is getting it in. Lifting a church floor is a major undertaking. In a medieval building, the floor slab often sits above centuries of burials and archaeological deposits. A faculty application will be needed, and the DAC will almost certainly require an archaeological watching brief or full excavation before any pipes go in. That can add tens of thousands of pounds to the project and months to the timeline.
The other practical issue is response time. Underfloor heating warms a large thermal mass - the entire floor slab - which means it can take many hours to bring the building up to a comfortable temperature. That makes it poorly suited to churches used only for a weekly Sunday service. It works best in buildings with regular daily use, or where the heating can run on a low background setting throughout the week.
If your church is already planning a major reordering that involves lifting the floor, underfloor heating is well worth considering. The electric version is fully net-zero compatible when paired with a renewable electricity tariff. As a standalone project, though, the disruption and cost are hard to justify unless the existing floor genuinely needs replacing.