You can get the client to disable this via the My Sky page here: https://secure.sky.com/mysky-homepage/indexb This is opt-in so they clicked a button somewhere when Sky asked them if they wanted adult content blocking. If anyone opts in to blocking; it's their funeral. It doesn't work. Sky's blocking even kills ThinkPad wiki.
Sky announced a couple of weeks ago that they intended to turn on their filtering by default. Maybe that's now happened. Source: http://www.bbc.com/news/technology-30896813
Don't get CloudFlare to budge you to another IP, you'll never know what may or may not be listed - most of the content on the default filter is not porn. This is Sky's problem, not CloudFlare's.
It's deplorable, but entirely predictable (and they were repeatedly and loudly warned!) that innocent bystander sites have been blocked by the censorship on Sky's broadband network that people haven't even asked for.
Have you perhaps considered legal action against Sky?
You may also want to let them know, but they can't admin the filter themselves (last I heard), so can't whitelist you, and the equipment they have cannot proxy the site on their list without also affecting yours. (That you share an IPv4 address is not itself an issue with CloudFlare.)
Don't mind me, I'm just getting snacks. This is going to get worse.