If you have the immersion heater on for most of the time, it is possible the bill could be £720, when you include the other electric usage.
The wall heater in the conservatory. Check to see the wattage of this. If you have it permanently on, with the thermostat turning on/off, it could be eating a lot of electricity.
Another issue may be the Gas warm air system. That is considered fairly old technology from what I have read and replacement is recommended by many. It may be worth looking into this.
I have seen an electricity meter being checked and it is a 20 minute job. They are not installing another meter to check the current one, but just checking that the meter does not appear to be faulty.
It is worth you regularly checking your own meter, when you have different electrical appliances switched on, just to see what appears to be using the most.
On the bills, it should show the meter number that they have checked and whether it is an actual reading or an estimated bill. It is estimated, then give EDF the correct current reading.