beany1:On do not want to help!
There are a pile of issues going on here and I sympathise with what seems to be Eon's very unhelpful attitude on a very complicated subject.
E10 is a complication which makes switching suppliers difficult or impossible so if Eon are charging you an E7 tariff go with that. On balance most people would be better with E7 than E10 unless they have a heating system specifically tailored to E10 and use it. Even E7 does not pay if you are never going to use your storage heaters and/or cheap rate water heating.
16,000kwhrs would be a total annual energy consumption in a reasonably well heated house. You say you "never have the heating on" and "don't have any hot water". Sorry something doesn't add up there. Either the 16,000kwhrs has been estimated by Eon, or there has been a massive catch-up on previous under billing or there has been some sneaky use of heaters, or possibly a billing error. A meter error is extremely unlikely.
Your bill may say you have used 16,000kwhrs in a year but is that what the meter says? Difficult to be more helpful without more information regarding the meter readings and whether the most recent bill or statement includes any estimated readings. Start getting a handle on your consumption by taking regular meter readings.
When contacting Eon with readings don't prompt them about the E10 meter, let the adviser control the process. There may be a time for sorting the E10/E7 meter issue but not until the 16,000kwhrs issue has been understood.