To return to your actual question though . . .
As an analogy, if the water meter out in the street shows that you've been using a swimming-pool-full of water every day, the water company will need to find out where the leak is. If it's between their meter and your property boundary they won't charge you. If it's on your property though you're legally obliged to pay for the water but the water company might use their discretion to reduce the charge.
Similarly, any excess electricity 'disappearing' on your side of the consumer unit (where your fuses or circuit breakers are located) must be paid for by you (although, again, the supplier might be prepared to exercise some discretion).
So if, for some reason, electricity is leaking to earth between the meter and your consumer unit, you shouldn't have to pay. However if it's leaking to earth (or actually being used) on your side of the consumer unit, they can bill you (but would hopefully use some discretion). Unless there's a fault with your consumer unit though (as well as with the wiring beyond it) it should be impossible for electricity to leak to earth on your side of the consumer unit, as that should cause a fuse to blow (or a circuit breaker to trip out).
It would be interesting to know that actual meter readings that you photographed (and the period of time which had elapsed between them), as we could then see just how fast you were allegedly using electricity.