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The easiest way to do this is opt in to marketing communications and then just phone up and go straight through to the I want to leave part. In my experience you don't get to speak to anyone useful when you call them so there's no point in having a discussion with them.
Put that in motion and at some point a few days later someone will phone you to offer a deal.
My last renewal took about 20 minutes: 15 minutes on hold before I said I was leaving and then a brief call when someone called me and asked what I wanted to stay.
I had the email - haven't seen any noticeable benefits (after restarting router) and still can't wait to go somewhere else. Price has risen from 45 when I moved in to 65 within 4 years. It's slower and more expensive with the same provider than my last house (350 speed for 35p/m).
However, I can't be bothered to wait on hold for 6 hours to tell them I'm leaving.