Cows hibernate in winter, grey squirrels are native to this country, conkers come from oak (or maybe beech, or is it fir?) trees, and of course there's no such thing as a leaf that can soothe a nettle sting. Or so, according to a new survey, believe between a quarter and a half of all British children. You can't really blame them: if, like 64% of kids today, you played outside less than once a week, or were one of the 28% who haven't been on a country walk in the last year, the 21% who've never been to a farm and the 20% who have never once climbed a tree, you wouldn't know much about nature either.

The survey, of 2,000 eight-to-12-year-olds for the TV channel Eden, is the latest in a string of similar studies over the last couple of years: more children can identify a Dalek than an owl; a big majority play indoors more often than out. The distance our kids stray from home on their own has shrunk by 90% since the 70s; 43% of adults think a child shouldn't play outdoors unsupervised until the age of 14. More children are now admitted to British hospitals for injuries incurred falling out of bed than falling out of trees.

Does any of this matter? In an age of cable TV, Nintendos, Facebook and YouTube, is it actually important to be able to tell catkins from cow parsley, or jackdaws from jays? Well, it obviously can't do any harm to know a bit about the natural world beyond the screen and the front door. And if, as a result of that, you develop a love for nature, you may care something for its survival, which is probably no bad thing.

But a growing body of evidence is starting to show that it's not so much what children know about nature that's important, as what happens to them when they are in nature (and not just in it, but in it by themselves, without grownups). Respectable scientists – doctors, mental health experts, educationalists, sociologists – are beginning to suggest that when kids stop going out into the natural world to play, it can affect not just their development as individuals, but society as a whole.

"There's a paradox," says Stephen Moss, naturalist, broadcaster and author. "More kids today are interested in the natural world than ever before; they watch it on the telly, they may well visit a nature reserve or a National Trust site with their families. But far fewer are experiencing it directly, on their own or with their friends, and that's what counts: this is about more than nature."

The American writer Richard Louv, author of the bestseller Last Child in the Woods, has defined the phenomenon as "nature deficit disorder". Something "very profound" has happened to children's relationship with nature over the last couple of decades, he says, for a number of reasons. Technology, obviously, is one: a recent report from the Kaiser Family Foundation in the US found that the average eight-to-18-year-old American now spends more than 53 hours a week "using entertainment media".

Then there's the fact that children's time is much more pressured than it once was. Spare time must be spent constructively: after-school activities, coaching, organised sports – no time for kicking your heels outdoors. Except kids never did really kick their heels. "I was out on my own and with my friends all the time, from the age of about eight," says Moss, now 50. "Climbing trees, building dens, collecting birds' eggs and frogspawn. Today, parents don't even want their kids to get dirty."

But the biggest obstacles to today's children being allowed out in this way (or even to the nearest park or patch of wasteground) stem more from anxiety than squeamishness. "Stranger danger", the fear of abduction by an unknown adult, is why most parents won't allow kids out unsupervised. Blanket media coverage of the few such incidents that do occur may have contributed to this; in fact, there is a risk but it's minimal – the chance of a child being killed by a stranger in Britain is, literally, one in a million, and has been since the 70s. "A far more serious issue, a massive issue in fact, is traffic," says Moss. "That has grown exponentially, and it's a very real problem."

It's a problem we need to address, because the consequences of failing to allow our children to play independently outside are beginning to make themselves felt. On the website childrenandnature.org, Louv cites a lengthening list of scientific studies indicating that time spent in free play in the natural world – a free-range childhood, perhaps – has a huge impact on health.

Obesity is perhaps the most visible symptom of the lack of such play, but literally dozens of studies from around the world show regular time outdoors produces significant improvements in attention deficit hyperactivity disorder, learning ability, creativity and mental, psychological and emotional wellbeing.

Just five minutes' "green exercise" can produce rapid improvements in mental wellbeing and self-esteem, with the greatest benefits experienced by the young, according to a study this year at the University of Essex.

Free and unstructured play in the outdoors boosts problem-solving skills, focus and self-discipline. Socially, it improves cooperation, flexibility, and self-awareness. Emotional benefits include reduced aggression and increased happiness. "Children will be smarter, better able to get along with others, healthier and happier when they have regular opportunities for free and unstructured play in the out-of-doors," concluded one authoritative study published by the American Medical Association in 2005.

"Nature is a tool," says Moss, "to get children to experience not just the wider world, but themselves." So climbing a tree, he says, is about "learning how to take responsibility for yourself, and how – crucially – to measure risk for yourself. Falling out of a tree is a very good lesson in risk and reward."

Ask anyone over 40 to recount their most treasured memories of childhood play, and few will be indoors. Fewer still will involve an adult. Independent play, outdoors and far from grown-up eyes, is what we remember. As things stand, today's children will be unlikely to treasure memories like that: 21% of today's kids regularly play outside, compared with 71% of their parents.

The picture isn't entirely bleak, though. In the US, nature deficit disorder is big news: Louv is delivering the keynote speech at the American Academy of Pediatrics' annual conference; city parks departments are joining with local health services to prescribe "outdoor time" for problem children. Here, organisations such as the RSPB, National Trust and Natural England are "moving mountains" to get families outdoors, Moss says. Often, though, this remains what he calls a "mediated experience" – dictated by adults.

One project, in Somerset, could show the way ahead. Two years ago the Somerset Play and Participation Service, a voluntary sector scheme run by children's charity Barnardo's in collaboration with a local authorities and a number of natural environment agencies, began putting time and money into encouraging children to play independently outdoors. Part of the scheme is a website, somersetoutdoorplay.org.uk, detailing more than 30 sites across the county, from hilltops to forests and headlands to beaches, where kids can play unsupervised.

"We aim for children to experience true free play," says Kristen Lambert, who runs the scheme's PlayRanger service. "Play that's not set up according to an adult agenda – in forests and open spaces, not designated play areas. There are no specific activities, no fixed equipment; there are tree branches and muddy slopes. The spaces themselves are inspiring. Children set their own challenges, assess their own risks, take their own responsibility, have their own adventures, and learn from them. And what they learn can't be taught. You should see them."