Hello there, this is what I intend to do if they carry on wasting my time.Yes, that is a clear indication something is wrong.
The "running even with the mains off" clearing means something is wrong. Given the usurious charges they talking about if no fault found, I would get an electrician in to inspect the cables and CU (consumer unit = fuse box) to rule out some unknown load / theft of supply, and if they confirm the meter is running with no load then you should have no problem in getting if fixed and hopefully the bills going back corrected.