Hi you say the plug and socket are OK.
I assume on one side of the heater the wire is wired direct to the economy seven socket and the lead on the other side is plugged into an ringed 13amp socket,that's the one for your neon light which only comes on when the heater is fully charged .You normally leave the convector set at number one,except in the evening you can open up to 5 but close it to number 1 before bedtime when the charge begin I think its around 00.30 until 07.00am
TommyB
December 2010