a regular meter reading was taken by the company every few months. T
Are you sure it was a physical reading and not just estimated?
Meter readers calling every few months is highly unlikely.
Logically, the systems are sufficiently sophisticated
You are talking about British Gas here - their systems are ancient and have no sophistication whatsoever.
A fixed direct debit has been taken each month and a regular meter reading was taken by the company every few months. The reading has been the same for 5 or 6 years it now transpires.
Take the average gas usage for a property and occupancy of the size hers is, and estimate how much gas would have been used over those years.
Some averages here:
https://www.britishgas.co.uk/energy/guides/average-bill.html
Compare that to their estimated readings over the years.
Estimate an approximate cost for that, and deduct whatever has been paid over the years.
What's left is what might be considered as what should be paid, assuming there is anything left at all.
As for complaints - do NOT contact BG by phone or email.
Send everything in writing, with their estimated readings, copies of ALL bills/other letters received from whenever the meter broke, records of what she has been paying, your approximations as to what may have been used over the period.
If they have been paying an amount each month which would be considered reasonable for a property of that size, then offer no payment. BG will have to void whatever the claimed outstanding amount is, install a new meter and start billing from the install date as if it was a new zero balance account.
If what was being paid every month is grossly under what would be expected (such as she was only paying £10 a month or something equally ridiculous) then she will have to pay something, offer some amount per month above what is being paid now.
For some additional info - at a unit price of 7p total (which is at the high end of pricing) and including the standing charge
8000kWh per year for small gas usage is about £55 per month
12000kWh per year for medium usage is about £80 per month
17000kWh per year for large usage is about £110 per month.