I have a lot of sympathy for the OP. Big firms are a nightmare,once the wheel has fallen off. They seem incapable of taking a logical view of it all.
Yep, I couldn't agree more, and it's unbelievably frustrating. The phone people are mostly following narrow criteria to decide what to do.
I once had an issue that may or may not be reassuring to the OP (long story, skip to the next post if you already know how incompetent big companies can be) where I tried to switch supplier *cough* npower*cough* and nothing happened. I called them 2 months later and told them not to bother, but they said I wasn't even on the system yet as they had a backlog. So they wrote a note to "pre-cancel" my switch.
Roll on about 2 months and I got and email saying they couldn't switch my supply due to an objection from the previous supplier, but they'd try again in a couple of weeks. I called and told them not to, and they again said I wasn't on the system anyway. Roll on a couple of weeks and all the emails etc for switching to them arrived and they set up a direct debit. Called them and told them to stop it, and they said it's too late and they'll have to switch me and then I switch again. I called the current supplier and they said they didn't get a switch request at all. So I cancelled the direct debit and hoped that was it...
I moved out shortly after that and settled everything with the actual supplier. Then roll on another few months and suddenly I started getting emails asking why I didn't pay the bill etc. I couldn't actually get through any of their security questions, and I couldn't manage to register for online account, so they wouldn't speak to me. Then I found in an email that the supply address was actually somewhere I lived a couple of years before and they supplied me for some time there! That got me through security, and they decided to send it back to the old supplier as an "erroneous transfer". The story is long at every stage but suffice to say the previous supplier refused to undo the switch, and they carried on hassling me.
Eventually they said they needed me to send them a copy of my tenancy agreement to prove that I didn't live there any more! I asked if they believed me or not, they said yes, so I said OK I don't care what you do, get a manager to look at it and sort it out, but whatever happens, do not call me under any circumstances. I was massively annoyed by this time as this was september and we originally tried to switch the previous november.
Anyway, fast forward a year, and suddenly I started getting debt collectors calling asking for some name that I knew they were using on that account (they still kept emailing me about the account, but addressing it to another name so I knew who it was) That went on about once a month for about 6 months, and then nothing at all.
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So the summary if you're still here, is their system only works in normal situation, and if something else happens they will basically act like it's your problem, but you can get past it with calm persistence. Just stay calm and keep explaining until they get it. If you like, going to Citizens Advice can be useful - they helped us a lot when our landlord left us with no safe heating for 7 weeks and no gas safety certificate (boiler was spilling, the wall was black around the break in the flue)