I was kinda shocked by The Guardian to be honest with you - I had a similar experience when I came to cancel my subscription to The Guardian Weekly, which is an excellent magazine.
In the end I just told my bank to stop the direct debit - I had a few what seemed like automated payment emails from The Guardian telling me that my payments had failed and to update my payment choices - but other than that I considered my subscription over.
Careful; if you don't go through their unsubscribe process, they can consider the contract still valid, and collect on the legally-still-valid subscription through liens and paycheck garnishments.
I had to stop payment via Amex to cancel WSJ. I have copies (and a receipt) of me informing WSJ that I was cancelling my subscription. Now I’m intrigued though. I’d love to see them try to claim there’s documented debt and collect on it.
In the end I just told my bank to stop the direct debit - I had a few what seemed like automated payment emails from The Guardian telling me that my payments had failed and to update my payment choices - but other than that I considered my subscription over.