Is that a real problem though? You did quote the accidentally after all. Both kids and adults have access to things they seek - whether that's going to be internet, magazine brought to school, or some other means. If they don't seek such content, they won't see much more than what's already available to everyone in the daily mail. I think the internet just made people aware of what's already been going on.
My questions would be "does porn prohibition create more good than the very likely government/school punishment for kids who will seek it regardless". (Once it's tracked and officially acted on, it's going to be a sex offender case like sexting became, right?)
(Also from my experience, things other kids did/said at school was likely more damaging and plain evil than anything I've seen on the internet so far. Kids have unrestricted imagination and are brutal. And I get the impression lots of parents forget what really happened.)
If you want to block porn at home, there are thousands of solutions for that. And they do work pretty well. If you're thinking of a global solution, I think it's just too dangerous.