Ivy and Albie arrive home from school and nursery, and slip through David and Katie Bond's kitchen straight out of the back door. After about 15 minutes, Albie, who is four, reappears, fist clenched. "Guess what I've got in my hands?" he asks. "Is it a worm?" guesses Helen, his grandmother.

"Do you want to hold it?" offers Albie, opening his hand to reveal a tiny, sand-covered worm. "We've made a horrible mess out there."

This hardly seems an exceptional scene, but it may be increasingly rare, and radical, for families today. Playing in the garden as a natural, daily event has only come about because Bond, who is a film-maker, has spent two years studying the declining role of nature in children's lives for a new documentary, Project Wild Thing. The wake-up call, he says, came when he taped a camera to six-year-old Ivy's head and recorded the time that she devoted to different activities: her days were dominated by playing indoors at school, car journeys and playing indoors at home. She spent just 4% of her time outside.

Bond calculated another staggering fact. His mother, Helen, who is 81 and lives with the family in London, grew up in Hornsea, Yorkshire, and at the age of 11 roamed across 50 square miles. When he was a boy, in the 1970s, he roamed within 1 square mile. His children wander freely only as far as their 140-square-metre garden permits and he admits that they are fortunate to have such a large garden in the capital. "We're so lucky compared with most Londoners," he says. "I own a tree."

It is difficult to decipher the precise constellation of social and economic changes that have made us afraid of nature, and curtailed a childhood outdoors. They are, however, visible through the lives of three generations of the Bond family. Helen was the eldest of three children growing up on the edge of Hornsea. Her mother was a full-time housewife but the children were left to play on their own – in the garden, the surrounding countryside, the nearby golf course and beach. They were outside as much as possible in all weathers, she remembers. "It was just a fun place to explore because parts of it were a bit wild."

It wasn't idyllic: the sea (where they swam unsupervised by adults) was brown, there was barbed wire and old pillboxes from the second world war on the eroding cliffs, and once, when she cycled the mile and a half to catch the school bus, a man exposed himself to Helen and her friend. Her friend told her mother, who said, "We all know they've got these things," and that was about it. Bond contrasts this memory with modern overreactions: Ivy's primary school recently circulated an email about reports of a white van seen outside school gates in the area and for three weeks the school run became a scrum until parents forgot about it.

Bond grew up in Canterbury in the 1970s. He did not roam nearly as far as his mother, but he played outdoors in the street with friends. Their favourite stomping ground was the local hospital. "We used to crawl through air-conditioning ducts and follow the pipes. It was an amazing adventure playground. We'd play dare, and see how far we could walk through the corridors before we were stopped," he says. There was no secure fencing or security guards.

For his film, Bond returned to Canterbury and talked to some children he found playing in his old street. "They were very gloomy about their level of freedom, talking about how the neighbours complain if they make a noise or play ball games," he says.

When a few children sneaked into the hospital grounds, the police were called. Computers arrived in Bond's childhood when he was about 13, and were a hobby; now, they are wallpaper. The children he interviewed in Canterbury celebrated extreme computer game-playing, in awe of a boy who devoted 10 hours non-stop to one game. "The bedroom was where they talked about having personal space and freedom," says Bond. "I didn't feel like my bedroom defined me as a child. My outdoor space did. My children will be much more defined in their psyches by their indoor space than my mum or I ever were."

When the Bonds moved into their house three years ago, they did something Bond is embarrassed about now – they drained the pond. Everyone told them horror stories about ponds and toddlers. "It felt like we'd been got to, in a way," he admits.

"Peer pressure is very strong," agrees Helen. "You think you can make the world afresh for your children, you think you can make your own rules for your children, but you can't."

Society's fears of the risks that lurk outside for children – from ponds to stranger danger – may be overwrought and irrational, but anxiety (the defining characteristic of British families, according to a Unicef report on child wellbeing) about traffic is more logical. The growth in road traffic is probably the decisive factor preventing children playing on the streets as they once did. The Bonds live on a quiet residential road, but the traffic is still relentless, says Bond. "Until they are a lot older, I don't feel comfortable with them cycling or walking around on the roads outside."

The headteacher at Ivy's school made the news when he asked parents of an eight- and 11-year-old to stop them cycling to school because of road safety fears. There may be new community efforts to close streets for children's play, but Bond fears these once-a-year closures "tie into the idea that outdoor play becomes an event and a treat. So much of our children's world has been turned into a treat by marketeers."

Irrational fears about risks, rational concerns about traffic, stricter policing of private land and loss of derelict spaces, the rise of computers and social media and the commercialisation of play. "It really is a perfect storm," says Bond of the factors stopping children roaming free.

David Bond and his children, Ivy and Albie.

He is convinced that fears over free-range children are not uniquely urban. Country children can be just as cooped up as city kids, and the latter used to wander in the nooks and crannies of cities as much as rural children explored the wilds. Nor are they a groundless middle-class concern. He found parents in tough urban communities who were equally worried about their children's lack of outdoor play; here, fear of crime was another inhibiting factor. In his film, Bond explores the role of commerce in encouraging everyone to stay indoors and wonders if nature could – and should – be marketed like crisps or computer games.

One insurmountable obstacle for parents wanting to send their children out to play is that all the other parents keep their kids indoors. In this environment, sending your children out to play, alone, without safety in numbers, would be "a lunatic decision", admits Bond. "It's like a Mexican stand-off – all the parents down the road are thinking the same thing."

So what can families do? There may be a growing awareness of the need to provide opportunities for outdoor play, but it can lead to nature becoming "an activity that is to be boxed up or controlled in the same way as swimming or music lessons", says Bond. "The pressure to work, to earn, to provide, makes you treat the outdoors like a product that you need to get down your gullet quick and consume, and that stops it being a place where you get what play theorist Bob Hughes calls 'soft attention'. You see the children do it – Albie gets lost in himself and the outdoors."

After talking to play experts, Bond is convinced that the best thing a parent can do is provide unstructured time outdoors. "It's slightly contradictory, but you have to plan to be unplanned." He began by identifying nearby places for unstructured play: parks, National Trust properties, wildlife parks. The Woodland Trust's website told him of all the woods in the neighbourhood, and then he found the ideal safe, wild and interesting place: Nunhead cemetery.

An old cemetery near my home is the place I take my daughters to play and explore the outdoors, but I worry that I will be told off for allowing them to frolic around in such an austere place. Bond has a rule that any tended grave must be left alone, but allows his children to clamber over the grand old graves. He is sure the generation beneath the soil would quietly approve. And he is less fretful than many parents about what others think.

During the snow last winter, he was ticked off for sledging downhill with Ivy too fast. Parents were afraid that he would collide with their children. What did he do? "I just had to dig deep and keep sledging," he replies.

Personally, I would struggle with such disapproval, but this episode illustrates nicely something Bond points out – that the battle to get children outdoors is almost entirely a parental one. What if children simply prefer to stay indoors? "It's mainly about persuading myself," says Bond. "Children left to their own devices will gravitate towards the things they love, and they love being outdoors. For every really miserable wet week, there's been some sort of amazing experience outdoors that we've had together," he says.

Children don't really notice the weather, but Bond realised that if he reacts to it, they quickly follow his lead, just as adult fear, of spiders, say, can be quickly transmitted. "I'm very determined that the children will face the risks and discover them," he says, although he admits that Katie is sometimes less relaxed about this approach.

For the Bonds, there are many fairly obvious benefits of having their children being active outdoors. On a holiday in the Yorkshire Dales, where Ivy and Albie played outside (in freezing conditions) all day, Bond noticed one result of great interest to any parent. "They slept well at night," he says, laughing.

On a recent country walk, Ivy admired some lapwings that "flew like a raggedy bat flapping about in a tunnel", she says.

"They are very good at pretending they are injured to lead you away from their nest," explains Helen.

The outdoors is a wonderful place to learn and Bond hopes to reverse the decline in knowledge that he has experienced – he knows much less about the wild than his mother. Bond struggles to distinguish between a snipe and a curlew; his mother will always know. She can also identify bones when they are walking the Dales and is able tell the children what is a rabbit or a sheep. When Bond and Albie were recently playing in Nunhead cemetery, Albie found a freshly severed crow's wing. It was still gooey, but Bond let his son play with it, and when they came home, they looked at the internet to find out how a wing functions.

Ultimately, though, the natural world is fun. Watching Ivy and Albie delight in outdoor play is uplifting. "The only thing that's anything like it is giving them a bar of chocolate," says Bond, describing their joy.

What does Ivy like to do best of all? "Outside play, field play," she says. Why? "There are huge blossom trees where you can run and catch the blossom. It's really fun. I like playing outside because I can meet my friends and today Bella gave me a piggyback – and I love piggybacks."

• Project Wild Thing is released in October. View the trailer here