It also raises the question of what counts as porn, which I think is a major, major issue here.
So I'm massively in favour of rape porn being illegal, that I think is a fairly obvious point to target. Also further crackdowns on illegal pornography in general, possibly including putting the onus more on the person providing the child with computer access, would be good.
On the other hand, the stuff on legal porn being censored I'm pretty dubious about;
1) pornography is classed as basically any sexually explicit matter used for sexual gratification. The last part of that definition is user-end so not in question here; if any erect penis or pair of exposed breasts counts as sexually explicit, then most of the main sites on the internet should be blocked by this legislation.
2) this confuses issues around pornography and implies that everyone who's ever seen tits on the internet is on a slippery slope to being a sex offender and in jail for the rest of their lives, and/or that it's unnatural or wrong for children during puberty to decide the other gender's genitals actually look sort of interesting. I think it is very wrong to give children lots of access to over-sexualised material, but it's also important that we don't end up with them all falling back on illegal and harder to monitor (and potentially nastier) porn sources.
3) This would just generally make more sense as an opt-in system. I think everyone should have the option of not looking at porn and parents should be helped to avoid showing their children, but I generally don't like assumptions of censorship first and ask questions later.
4) "Studies suggest the filtering systems can be fooled quite easily and present no real obstacle to anyone that can use a search engine." - BBC News. How the hell is this going to work and who's liable? No practical solution has been suggested.
5) For softcore porn in particular I really don't think it's up to the government to decide what should be socially normative. Some (probably most) porn is demeaning to women, I don't doubt, and that is wrong. Some gives a very messed up view of sex and relationships, too, which is equally problematic. On the other hand some of these things we've got to deal with as a society not by clamping down but by creating and working with cultural norms.
So tl;dr version: cutting back on nastier forms of porn good, autocensoring legal porn impractical as a system and moreover could have negative unintended consequences.