VM appear to have made cancelling their services as tedious and troublesome as they possibly can, and you're not alone in this - there's many other examples in this forum, although there's also many people who manage to cancel without hassle. the resolution of this is not likely to be quick, I'm afraid.
You gave an instruction to cancel, it was not processed and as a result VM are in direct breach of Ofcom and CMA regulations, as well as the whole panoply of UK contract law and consumer protection law. In terms of getting call recordings, if you've made a request, VM have 30 days to comply, if they haven't then notify the ICO, as VM have previously been told that if they didn't improve their performance on subject access requests they'd be fined. If you need to request this again, then the online form is here.
Now read and follow the VM Complaints Code of Practice. I always recommend putting complaints in writing and sending by recorded post because VM have a history of poor handling of telephone complaints, and of web complaints not being properly submitted. You may have zero confidence in VM's ability to resolve a complaint, but the point is that you have to follow the process if you are then to escalate this to the industry complaints adjudicator. Your complaint would ask (a) backdating the cancellation to when it should have been effective, (b) refund of all payments they've demanded since the cancellation date that should have applied, (c) correction of any credit history foulage if this applies, (d) payment by Virgin Media of significant compensation for the poor service, failure to process the cancellation, any wrongful credit history reporting, and the inconvenience and distress of having to sort out VM's mess. If this gets a good outcome then the job is done, but don't expect that - VM's complaint handling is outsourced to International Imbeciles plc, so expect to be fobbed off. When that happens, then you can reply to any "resolution" letter by rejecting that and asking for a deadlock letter. With the deadlock letter you take the matter to Ombudsman Services (any references in VM documentation or other posts in this forum to the alternative adjudicator CISAS are now out of date), making the same requests, and adding a further compensation request for VM's failure to resolve the complaint competently. You may wish to additionally report your soiled credit history as a result of VM's failure to process a cancellation instruction to the ICO because this means VM have been processing inaccurate data about you - that's a breach of GDPR.
Make sure your complaint is clear, starts from the beginning, includes as much detail as possible on the contacts you've had with VM, including (if relevant) any rudeness or being cut off or disconnected. It should also specify exactly what you want: Refund of any over-charges, correction of the credit history, a generous "goodwill gesture" (compensation) for the hassle, wasted time, broken promises and sheer unpleasant inconvenience of the whole thing. If the forum staff can grab this and get it sorted that will be quicker and easier for both parties, but don't settle for any compromise or inadequate goodwill gesture just because it's easy - and VM have a miserly track record on voluntary goodwill payments, don't let them off the hook. I'd suggest that you're looking for a good few hundred quid compensation for the very serious inconvenience and distress.
Do let us know how you get on, whether through formal complaints and adjudication, or by some resolution sorted by the VM forum team. If you go to adjudication there's usual a non-disclosure clause, but that covers the detail, you can still let us know if you're unhappy, satisfied, or very satisfied with the eventual outcome. And don't settle for VM sorting the credit history but paying you a hundred quid by way of restitution - their failure is very serious, it's a repeat failing in these forums, and the consequences for you have been financial harm and distress.
