The CCC isn't wrong (I assume), the poster that TazeTSnitchzel was replying to is wrong. The CCC's website is, according to them, caught up in the content filters that all ISPs now provide as an optional service, which block things from pornography to filesharing and gambling sites.

The majority of people in the UK are not currently under this filter, and the rest can opt out if they choose to do so. This is not the case with court-blocked sites like The Pirate Bay.