Good morning, new to community looking for help with final bill.

Renewed my Virgin Media broadband contract on 20th September and signed up to another provider on the 2nd of October ( during the 14 days  cooling-off period) as they gave me a much better deal. The new provider notified Virgin Media that I will be switching to them on the 9th of October, Virgin Media sent me an email on the 2nd of October with switching ref number  clearly stating that I will be switching ti another provider on the 9th and there will be £0.00 early disconnection charge. On the 11th of October VM sent me my final bill including £534 early disconnection charge. Called VM and they argued that the disconnection date was outside the 14 days  cooling-off period witch I think that unfair. They kept passing me from one department to another with no other outcome apart from me having to pay. Sent email to the ceo.office and no reply, cannot use web submission complaint as my Virgin  account has been disconnected, it seems like I am stuck. Any advice would be greatly appreciated. Thanks in advance.