AT, you’re using gas, you know it doesn’t come free, and the power company are entitled to charge you for it. The only debate is over how much you should pay if there are no metre readings. Power companies tend to be reasonable and go for an average if you have the info to work it out.
In your case, you could use historical data or come to a mutually agreeable amount. Your problem is that you have been running up a tab, so the rate you are charged may be reasonable but the lump sum catch-up payment may be hard to wear. They will probably agree to spread the cost over enhanced monthly payments until the backlog has been paid.
If you are ignored and action is not forthcoming, keep a record of your communications and keep trying. It will establish your good intent and will help when an eventual figure is decided.
A mate of mine spent 2 years chasing the company with a similar problem and eventually wrote stating that he would assume all power use was free as his attempts to pay had been consistently spurned. He carried on that way for SEVEN YEARS until the company caught on. He agreed a goodwill payment of £500 and to start from scratch. Not bad considering it was not just a domestic supply, but also powered his farm.