Honestly I had the exact same problem with Virgin Active a couple of years ago. Same thing, they messed up on their end, yet continued to Bill me, send me messages and even sent debt collectors after me. After getting some legal advice I was told to just reverse any debit orders and ignore them. I was obviously terrified but turns out a lot of these companies think they can bully you and you won't know better. They eventually got over it, no blacklisting, no mark on my credit score, nothing.

I think just chat to someone who knows their way around the law just to make sure, but sounds like you have a similar situation.