Wrong end of the stick...
The UK Govt has never said that it will fix the problem. What it will do is prevent people seeing the content inadvertently - which is a good thing given there is no defence to ownership of child abuse images.
Having built systems that address this sort of area, you cannot block access. There are too many way to subvert any of these systems through proxies, using more obscure protocols and even not using the Internet at all (this is not a new problem - the Internet just provides a more efficient distribution mechanism).
WRT civil liberties, I know for a fact that the IWF and related organisations are not at all interested in filtering the Intenet per se. It's just about controlling and limiting access to illegal content as defined by the government in law. The IWF is also a charity - funded by a fairly diverse group of members so probably has more regulatory oversight than most other organisations carrying out relted activities.