@Ohsugarhoneyicetea
Flag it with them now that you think your meter is faulty. They are supposed to do a physical check at least every two years, so figure out when this last was as they have obligations too. And they cannot back bill you for more than a year, so if the under charging has been going on years and they havent checked the meter they are to blame too and wont get all that money back. Also there could be a fault. Get the problem sorted now. The cost is going up hugely soon and you want whatever usage you have based on old prices not new ones.
I think the max of 12 months for backdating charges only applies if they haven't been charging you at all, not to under-estimates.
I had a client who'd been using gas for years, and never had a bill. We'd tried to get an account set up several times, but the MPAN service flatly denied that there was a gas supply to the property, even when we gave them the meter number. The CAB assured him that, because he had never had a bill, they could not ask him to pay for more than 1 year's consumption.
I suspect that you've not calculated the consumption correctly OP, that is a massive amount. Is it a digital meter or one of the old ones with round dials? If you post a pic of the meter with the readings, I'm sure someone on here will be able to work out what the actual reading is.
The amount you've quoted is more than I'd use in 25 years, based on my consumption for last month.
They will have to agree an arrangement with you where you pay the current charges plus a chunk towards the arrears each month, they can't possibly expect you to pay all that in one hit. I would also argue that they have a duty to check your meter now and again, so not entirely your fault, and that as a lot of that energy will have been used when prices were much lower, they should reduce the total cost to reflect that.
If your meter is in a place that's hard to access (mine is in a cupboard you have to crawl into) you could argue that it was unreasonable of them to expect you to read it yourself, although that may not wash if you're young and fit.
When did you last get a bill based on an actual reading?