If the rep you talk to won’t do it, hang up and call again.
"Can I get the new customer rate"
"No that is only for new customers"
"Okay I'd like to cancel"
"Great, anything else I can do for you today"
"Sure, I'd like to sign up for new service"
I tried doing the chat to cancel. I said multiple times that we wanted to cancel and the person (presumably a person following a script, although they certainly seemed robotic) just kept ignoring that. Eventually I said I'm cancelling, if you charge us, I'll charge it back and took a screenshot of that.
When they charged me, I charged it back. No need for the screenshot, which was mildly disappointing because this was one time where I felt I had proof that I tried to cancel.
We'll never subscribe to The Economist again. If you make it this difficult to leave, better not to start.
Immediately after my subscription expired they started emailing me 1/2 off offers. The whole experience put a bad taste in my mouth and I won't be back.