I am a meter engineer who predominantly works for BG and stumbled into this forum looking for something else. Whilst I'm no billing expert I can see you have a problem that I have encountered before.

Firstly, it looks like your clock on the timer has stopped in the low rate area, this timer type is designed to switch the meter to low rate and switch the supply to the storage and immersion heaters at the same time. If the storage heaters are switched on it is the elements that will be heating the house through the day and not the bricks! This will significantly increase the amount of electricity being used and will make it difficult to correctly 'guestimate' a correct reading for billing.

As said earlier I have seen this before, and you need the meter changed ASAP. The new meters have built in clocks so the old one you have will go. This fault is extremeley rare (I've only seen two in the last 3 years) make sure that the next time you speak to BG that you mention that the heaters have been on all the time, they tend to be pretty fair when they come up with a figure, and this may help them.

If storage heaters are no longer fitted it is possible that the electricians doing the work disconnected the supply to the clock when the heaters were taken out....this is a lot more common than the clock going U/S. When the clock loses it's supply it has a mechanism within it to keep the clock working (a back up in case of power cuts). This eventualy runs out and the clock stops, could be on high or low rate, this may be what has happened if no storage heaters are fitted.

Hope this helps. Let us know how you get on with the visit today, be interesting to know what has been done.