A bit of online browsing led me to far infrared heaters, with an inevitable sojourn into those made with Graphene. For those who aren't familiar, Graphene is a certified wonder material which could one day change the world if the horrendous cost of manufacturing it can somehow be addressed (fusion's just a decade away etc etc).
Far Infrared heaters come in various shapes and sizes, but do tend to be a large panel which may or may not fit in with the "feel" of the room. However, such heaters can usually be painted - with the result that some suppliers sell pre-made infra-red wall art (a picture that heats you, neat).
I decided that an Infrared heater might be quite well suited to our needs. However, I didn't want to start by spending out on a large panel (and also had some unhappy noises directed my way about "big ugly panels"). So I decided to start with a hanging heater not unlike the one linked to above.
The radiators are run by the central heating, which does a good job of getting the rest of the house warm. Unfortunately, because of the knock through into the next room, it's a large (and often draughty) space.