Last year, when Tanya Byron issued a call for evidence for her report on child safety in the digital world, hundreds of children responded. One was a nine-year-old boy who told her: “I'm worried I'll get lost on the internet and find I've suddenly got a job in the Army.” Only the combination of a young mind and a parallel digital Universe could produce such a deeply contemporary anxiety. But there are signs here of parental input, too; warnings of online press gangs issued in good faith but total ignorance, perhaps, or scaremongering by a parent desperate to distract a child from the real risk of stumbling on a massively multiplayer online version of Grand Theft Auto, in which players impersonate psychotic criminals armed with machine pistols and baseball bats, stealing, killing and having sex at will.

Video games and the internet can be as frightening for parents as for their children. That is why the Byron report is both important and overdue. It makes worthwhile policy recommendations, including calls for a new council for child internet safety and for video game classification to be standardised along feature film lines. It also takes its remit of improving child safety so seriously that a young readers' version has been published alongside the full report.

Those young readers will approve of Dr Byron's starting point - that the digital world offers “incredible opportunities for having fun, learning and keeping in touch with friends”. But her most important conclusions concern parents. Too many find themselves on the wrong side of a generational digital divide, unsure what their children are finding online, how it is affecting them, or how to control their access to it.

This is a divide that the middle-class tendency towards having children later in life may widen. Yet online, as in the real world, parents remain the most important gatekeepers to their children's minds. Ignorance of what the cyber-Universe contains and how it operates is no excuse: the single greatest danger for a child with a keyboard and a mouse is a parent with head stuck in the electronic sand. In principle this means a duty to trawl the sites and play the games to which children are drawn before deciding whether to ration or veto them. In practice it might be as simple as activating a “safe search” button on the Google homepage, or switching on the blocking mechanism on a Wii console.

The report is not authoritative on the effects of websurfing and video games on children's minds. It cannot be. Reliable, long-term studies are still too scarce. But, despite its optimistic tone, it broadly endorses four main concerns: that violent video games can induce violent, real-world mimicry; that anonymous internet chat can turn swiftly to amoral internet bullying; that games and net activity alike suck up time that might otherwise be devoted to less sedentary, more social activities; and that young children especially struggle to distinguish virtual from real as their frontal cortices develop.

It was not part of Dr Byron's brief to study the notion that parents may have started using the internet as an unpaid childminder. Nor does she presume to remind them that libraries still offer more than Wikipedia, and that tennis, unlike the PlayStation version, involves real exercise. But her plea for parental responsibility is timely - and it applies offline as well.