The sight of young people gathering on streets and in shopping centres is one of the things that can create alarm or suspicion in adults, who think such groups are going to be abusive or extreme in their behaviour. But today's report from the Good Childhood inquiry ought to challenge many popular misconceptions about young people and our shared public space.

Set up by the Children's Society in 2006, the inquiry has so far reported on children's attitudes to friends, family and learning. What may come as a surprise in today's findings is that many young people themselves feel that they are not safe or welcome in public places, sometimes because of aggressive gangs colonising these places, but also sometimes because of unfriendly adults. Hanging around in groups is often a way for many youngsters to feel secure, rather than a way of menacing anyone else. And the discouragement of games in public places intensifies the problem.

The inquiry's earlier reports had few surprises - children value their friends, want stable, loving families with a proper parental presence and expect schools to be supportive and free from bullying.

Perhaps today's report will pose the toughest challenges so far. Its findings are about lifestyle, and they deal with, among other things, attitudes to alcohol, drugs and sex, revealing that the vast majority of children and young people approach these issues with a high level of common sense. But the lack of safe public space - where the young can go and gather, away from both school and home - is a striking and repeated complaint. Leisure facilities targeted at the young are often hopelessly under-resourced and, for children living outside the urban or suburban environment, the cost of public transport means that the options are severely limited.

All parents know just how much of a flashpoint the question of having your own space can be. But the issue is just as acute outside the home - perhaps especially for young people whose home circumstances don't allow any real privacy. The withdrawal of young people into e-communication, from computer games to permanently attached mobile phones, is much lamented and maligned, but is partly about the desire to be inside a protected space from which adults are excluded. If the world comes to be seen as territory where the casual presence of the young is not welcome, it is not surprising that the indoor, electronic world is more attractive.

But, as the report's findings show, children still value actual physical companionship - which is why they want places to meet that really belong to them, or at least don't belong to adults who want to exercise constant and critical scrutiny. This ought to make us think a bit about what makes public space feel unfriendly to the young - and to realise that this includes the attitudes of some adults. The use of ultrasonic dispersal devices - the Mosquito, audible only to those under a certain age - is a sad example of an indiscriminate and knee-jerk response to a perceived problem, which only deals at best with symptoms, not causes. The Buzz Off campaign against these devices, which is strongly endorsed by the children's commissioner, deserves wide support.

Open space, in park or street, is something we in the UK have not been good at handling in the past decades. Some urban development has created desolate and uncared-for cityscapes, in which people do not want to spend time and which are distant from where anyone lives. An uncared-for environment invites vandalism, and a downward spiral is set in motion. Our Victorian ancestors thought a good civic landscape had parks, dignified public buildings and reliable public transport - all things that gave people a feeling of proud ownership in their community. If we now hear young people lamenting the lack of safety in, and availability of what should be, public space, it is a predictable result of years of indifference to its importance for us all.

Political parties agree on the need to reclaim public space - making parks and playgrounds safer with non-intrusive adult supervision. The urgent need for investment in decaying youth centres and the provision of new, possibly mobile, facilities is also recognised. A few years ago the Soul in the City project drew in thousands of young volunteers in Manchester and then in London, reclaiming uncared-for space, such as half-derelict adventure playgrounds.

One of the recurring challenges is to find a way of safeguarding young people's space without policing it in an intrusive or humiliating way. Adults must think twice before assuming that every group of under-20s in a street or mall is likely to be a threat. We must work out what skills are required to provide realistic supervision, what voluntary help may be needed to support safe environments and what transport policies might best serve the needs of isolated young people in rural areas.

The issues raised in the inquiry's report concern us all. A comprehensive look at our expectations of urban life and space, and at how we can tackle the isolation of rural living, will help young and old alike. The inquiry can hardly do its work if we aren't prepared to look into what makes a good adult life too.

· Dr Rowan Williams is the Archbishop of Canterbury and patron of the Children's Society Good Childhood Inquiry