Apparently the next step is reporting us to OFCOM if we do not comply.
They also say their decision is final and so no need to send them anything more.
We do plan to dig out all the proof of their factual error in claiming that the customer asked to cease the service. They should consider a factual error. We have told them once and they ignored us.
We don't believe the customer asked to cease, and later emails discuss both the price of the ongoing service (stopping "premium" on the lines) and stated "we wish to continue with the service". They also used the ongoing service.
One of my biggest gripes is that a dispute over the date they asked to cease does not exist! The customer has not disputed this to us. They have simply included it in an ADR claim. So we have not had the chance to resolve the dispute.
Confusion over cease dates is something we sew up very well in our terms - we provide a "receipt" by way of a digitally signed order confirmation, and if the customer cannot provide the order confirmation (or number thereof) then they have to pay the ongoing charges. If they can, then we correct our error. It is a simple one to resolve.
Anyway, I think we probably need to ask OFCOM about this. They are the ones requiring us to comply with a decision made in accordance with the scheme rules (which we assert is not the case here).
At least if we are asking OFCOM we preempt being "reported" to OFCOM.
However, I am trying to get some legal advice on this.