Oh, so you want the government to police people's kids' internet usage 24/7, inadvertently screwing everyone else over in the process? I'm sure this will end well for the UK, especially the economy.
No one. Nothing should be done. If parents aren't going to do anything, what's stopping the kid from getting the parents ID when they're not looking? Or better yet, the same parent which verifies the site for the kid just to get them to shut up? It's the same parental group.