Hopefully this has been sorted now situation seems to be as follows:
The property has, or at least is equipped to use, Economy 7 or similar electricity tariffs where all consumption in the off peak hours, typically 00:00 to 07:00 GMT, is at a cheaper rate. The meter has two readings, one (Low) for consumption during the 7 hours and another (normal) for the other 17 hours. There's a mechanism to switch the supply over at the appropriate time. At the same time it connects the discrete circuit for the Storage Heaters,
In reasonably recent (like last 20+years) set ups the switch is effected by a radio signal from the Electric company. It's pin point accurate and adjusts doe Daylight Saving Time.
Prior to that there was an electromechanical clock, often branded Sangamo, which effected the switching mechanically. The clock's time base pre-dated quartz and was probably the 50 cycles/second mains frequency. Not uncommon, at least in rural areas, for the mains frequency to be unreliable. A relative in a Worcestershire village gave up with their cooker's timer/clock because it drifted off time.
Two things to do (1) check you're actually on an E7 tariff - I've heard of people having an E7 meter but a standard single rate tarrif. Meter reads as the sum of both rows (2) ask for your metering to be updated. If you're getting cheap rate 'leccy at peak demand time the supplier will be keen to get that put right.