I've done this using my credit card company (not the bank) and they were very helpful. I explained why I wanted them to stop the recurring payment and they asked if I wanted to dispute any of the older charges, took less than 5 minutes. I call the 'fraud/disputes' phone number on the back of my card for this and I think that is not the bank, I think it's Visa / Mastercard themselves.

I bet processes like this are why subscriptions like gyms are starting to require your _bank account info_ rather than just a card.