How would an ISP block them, however? The only mechanism I know about would be DNS blocking, whenthe DNS server is supplied by the ISP.. Is there some new British trick where pages of certain sites could be selectively blocked? If so, how long before "politically sensitive" human rights pages would be blocked, or whistle blower pages?
CleanFeed, built by British Telecom to block access to child abuse imagery, sold to other ISPs, then inevitably abused as a blunt instrument to enforce copyrights. It's a two-stage filtering system: a list of IP addresses gets loaded into the ISP core routers, which diverts all access to those addresses through a proxy server; that server checks against a (secret!) list of prohibited URLs and lets the rest through. It has already blocked part of Wikipedia by mistake or misjudgement, and the government has already announced plans to filter "extremist" websites too.
TalkTalk, another of the named ISPs, bought a more elaborate setup from the People's Republic of China for millions of pounds, and push their "adult" content censorship system on all customers who don't specifically opt out. It's been a big political issue lately, with the current government wanting to force all ISPs down that route so you'd have to ask your ISP specifically to stop filtering your connection.