We techie types know that trying to censor the Internet is like trying to collect rainwater in a sieve. However, politicians don't understand the Internet, and are almost pathologically unable to say "no" if the subject at hand has ever been linked to any sort of problem for children. Thus, our politicians believe they, and they alone are the only people who can save the UK's children from the perils of the Internet.
The Internet seems less convinced. First there was the Tor Project. This is probably the biggest thorn in the side of any government trying to censor the Internet. First of all, if you use it right, it makes your Internet communication untraceable, but Tor is an important 'freedom of speech' tool that even the most despotic governments around the world struggle to ban. As such, it's going to be a while before the UK government tries tackling it. Incidentally, my local MP hadn't ever heard of it, which I suspect is pretty common around the Commons. By now though, I expect just about every 14 year old boy in the UK knows all about it.
One I just heard of today is the aptly named Go Away Cameron. It's a Google Chrome extension that figures out if a site's been blocked and works around it. It's a lot easier to use than Tor, but it's probably not quite so safe - that said, it's probably enough for most people.
I just did some searching for sites that have been blocked. I couldn't find a list, and in fact all the results I could find list sites that have been mistakenly blocked. Here's a nice round-up:
Sex education websites, Top 10 Sites Blocked by Filters (including great ones like shelfappeal.com and ehow.com), The Scunthorpe Problem, Childline and others, and The BNP Website.
All these of course get plenty of media attention and get unblocked pretty quickly. What about the smaller sites, or the ones that are controversial and so not so obviously over-filtered? The problem is, the government just made itself liable for all of this (even though they claim it's the ISPs that are responsible).