Where's the crying Statue of Liberty? Or, I don't know, Margaret Thatcher?
Seriously, this is old news from 2013, we called it the Great Firewall of Cameron: I talked to Theresa May about this, personally, and RevK submitted evidence about it (and his ISP, Andrews & Arnold, just flat out doesn't do it - if you want filtering, he says, fuck off and choose a different ISP).
She's a real bitch, and now she's probably going to be Prime Minister. We are so fucked.
However, everyone's supposed to be asked if they want blocking or not when they sign up. You opt out, it's gone... except they do have the equipment still, so some torrent sites like The Pirate Bay (a good canary for this shit) are still blocked - those mandated by the High Court because they do have the equipment, so the Court figured it could make them use it. Oh, and those on the Internet Watch Foundation's block-list: those are URLs flagged as containing child porn, although honestly the vast majority of the domains uncovered by my research (which, by the way, does not visit any websites, I don't want that shit) are expired, invalid, or just plain look spammy, they seem to have a very short half-life. I haven't seen any obvious mis-listing on the IWF list, except notably that one time they blocked Wikipedia because of the Scorpions' album cover, which was arguably technically correct, but obviously bollocks and swiftly withdrawn before they ruffled too many feathers.
Sky's blocking is broadly speaking based on BT's "Cleanfeed" - an IP-block-level transparent proxy that uses ARP poisoning. Affected IP blocks have port 80 forwarded via Squid for URLs that don't match the filter; it returns either blocked pages or 404s for others (instead of the correct 451 or 403 status code). It can be circumvented by numerous techniques, including most VPNs, Tor, and a few others I won't talk about here. It can be mass-exploited to redirect or inject … actually no, not gonna disclose that either.