Hi Tillyella
Unfortunately, other than giving general advice, there is not much your supplier will be able to do. They are responsible for the electricity supply up to your meter, nothing after that. So clearly the electricity is getting to the meter ok, so their responsibility ends there.
If the meter was faulty however, they would investigate that. It doesn't sound like it is faulty to me though. you can request they come round and check it, but you will be charged for this if no fault is found.
If you had any new appliances, it is possible that they are sapping your electricity. Other than that, it is difficult to know what to suggest. Are you sure that your previous bills had been based on actual meter reads, not estimates? if they were estimated, it could have been that your previous bills were slightly too low, leading to a larger catch-up bill once an actual read has been taken.