Unfortunately, this post is confusing two very different things, which means the headline is totally wrong.
The site checker that the "grumpy old BSD guy" linked to is related to o2's mobile service, not its broadband service (which is now part of Sky). In common with most mobile companies, o2 has a default blacklist, which can you opt out of easily. It also has a set of much stricter "Parental control" setting which allows parents to tightly lock-down what a child with a mobile can see. It's this second "Parental control" setting that's basically blocks everything on the internet, apart from a handful of "child-friendly" sites.
I think this isn't anything to do with the government mandated porn block. It's just the same mobile filtering that's always been there, and that's common across pretty-much every mobile company. I can't imagine why anyone would change any child's mobile to basically block the whole of the internet, but it's opt-in, and it should be up to the parents.
Sky, which now owns o2's former broadband service (not the mobile network), does have a system of DNS-based filtering called "Broadband Shield" which is compliant with the government-"requested" filtering system. Although I haven't run through it, it seems to work like this: when you sign up to Sky as a new customer, you're presented with filtering options. The default setting is on, but you can change it at this point. (More details in Sky's response to ORG's questions about it). The "PG" and "18" level filtering is, of course, as much riddled with inconsistency as any other filtering system, but it's not the "OMG BLOCK EVERYTHING" that o2's mobile parental controls are.