I have had a similar problem with SWEB on a house I used to own. It had two electricity meters, one peak and the other Economy 7.
They had to replace both meters as to service the old ones. Prior to the change we had both meters read and a bill stating both readings supplied. After the change they lost one meter from their system. So that the meter reader could see two meters but could only read one. This went on for a couple of years with us telling SWEB about the problem almost monthly and their help desk telling us that we must be seeing things as we only has one meter. We even had SWEB managers come out and go yes you have two meters, we do not know why you are not billed correctly. In the end SWEB wrote off the bill outstanding and paid back what we had payed as compensation. A total bill writen off of over £1000 for over two years of electricity.
If I was you I would talk to one of the energy watchdogs, as this is what we did. They applied presure to SWEB to sort it out. You might not get the whole bill writen off but I would push for it as teh mistake is British Gas's, not yours and you have pointed out their error to them.

Since moving in to my new house, I have not received a gas bill but have had electricity bills from British Gas.
I have talked to customer services who have told me they will organise a bill that I should expect within five days. The operative told me that British Gas should have billed me within 3 months and that as I have already started the ball rolling to switch over to Scottish and Southern that British Gas will have to allow me a payment plan to pay off the expected £300 bill or they will offer me a discount if I pay in one go.
What I want to know is whether anyone else has had experience of a discount of this type. I have no idea what they may offer. They agreed on the phone that the mistake was theirs because of the new billing system just introduced. They never closed the account from the previous occupant, or set up my new one despite being informed at the time. They managed to organise the electricity accounts.
Any info would be helpful.