Storage heaters contain ceramic bricks or other dense material that absorbs heat from electric elements overnight, when electricity is cheaper on an off-peak tariff such as Economy 7. During the day, that stored heat is released gradually into the room. Modern versions have fans and better insulation to give more control over when the heat comes out, but the basic principle has not changed in decades.
The fit with church use depends entirely on when people are in the building. Storage heaters charge overnight and release heat during the day, which works well for a community hall or church office that is busy on weekday mornings and afternoons. It works badly for a church that is empty all week and needs to be warm for a service on Sunday morning - by then, most of the stored heat will have dissipated into an empty building.
In a listed interior, the physical bulk of storage heaters is a concern. Even modern slimline units are deeper and heavier than a standard radiator, and mounting them on historic walls may need faculty approval. They also need adequate electrical supply, which in an older building can mean rewiring.
If your church doubles as a weekday community space with regular daytime footfall, storage heaters on an off-peak tariff can keep running costs manageable. For the typical pattern of Sunday-only use, the timing mismatch makes them one of the less practical options.