Assuming she has it, is there a CH pipe relatively near the room?
Yes there is, just the other side of the wall in the kitchen directly where the new heater will go, put there deliberately for a radiator in the conservatory. However
.....
1. When the conservatory was built, it was part of a larger kitchen extension project, and the LABC inspector said that we could not have a radiator connected to the central heating system installed. ...
2. There isn't a lot of space available, just about the size of a wall mounted electric convector, so only a small radiator would be possible anyway.