If VM are maintaining that you agreed a new contract at some point, then they will have the records (call recordings, chat sessions, or paper documents) to prove it. Based on what I see in this forum day in day out, I'm more inclined to believe your version of events, because unagreed contracts and unagreed contract terms are regular complaints here, thanks to Virgin Media's poor staff training, poor business ethics, poor compliance, and poor handling of complaints.
I would suggest you raise a Data Subject Access Request with VM, asking for ALL detail they hold on you including but not limited to call recordings, chat sessions, paper documents, and any proof of the contract they're now saying you have at some point agreed to. See what turns up. In the meanwhile, don't stop paying, that'll cause problems with your credit history, and even if VM are at fault, it can be even more stressful for you to sort out.
I'd suggest DSAR first, then follow VM's formal complaint seeking compensation (if you haven't already), and if VM don't agree to sort it out and settle on generous terms, reject the "resolution" their complaints team offer and ask for a deadlock letter. With the deadlock letter you escalate the matter to CISAS, who take these matters a lot more seriously than VM's Laurel & Hardy customer service do. In terms of the compensation, I'd be pitching for at least £500, given the seriousness of putting in place a contract you didn't agree and then the utterly farcical performance since then, I'd also demand VM clean up the credit history mess they've made. I'd say you should complain to Ofcom (they don't intervene directly, but will review such complaints with VM, and also consider raising the matter with BBC TV's "Watchdog" or Radio 4's "You and yours".
Staff here may offer to sort this out, if accepting any offer, make sure any settlement is comprehensive, complete and extremely generous.
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