At what age should children be allowed to cycle unsupervised? For paranoid parents, maybe never; for others, perhaps nine or 10. But for one south London couple it's even younger: Oliver and Gillian Schonrock allow their two children to cycle to school together – aged only five and eight.

Not for much longer, perhaps: the Schonrocks were censured last week by their school headteacher for allowing them to ride unsupervised the mile-long distance between Alleyn's junior school and their Dulwich home. The Schonrocks say they merely want "to recreate the simple freedom" of their own childhoods; Alleyn's headmaster Mark O'Donnell thinks it might be a matter for the social services.

Who's right? For the department of education, it's a grey area: there are no official guidelines. But for Oliver James, child psychologist and author of parenting manual How Not To F*** Them Up, the issue is more clear-cut. "I'm pretty gung-ho when it comes to my five-year-old," he says, "but I wouldn't let him ride alone. I think it's a pretty odd thing to do. It should be banned really, though I couldn't say at what age." James is also concerned that the Schonrocks' children are at risk from attack. "Not from adults – there's a huge exaggeration in people's minds about paedophilia – but from other children. It depends on where you live, but other children pose a genuine threat in terms of knives and muggings."

Justine Roberts, who runs parenting website Mumsnet, is more worried about the cars: "For me the biggest risks aren't the strangers, but the traffic. Personally, I wouldn't let my four-year-old cycle to school even with me in tow. But all children are different, and in the end we ought to trust the parents."

According to Professor Frank Furedi, a sociologist known for his opposition to paranoid parenting, the Schonrocks should be praised. "Riding along the pavement is obviously well within the capability of many eight-year-olds," he says. "And some five-year-olds will definitely be mature enough to start to go to school on their own. Of course there are some children you wouldn't even let near a bicycle, but it sounds like these particular children will have benefitted tremendously from the responsibility."