Local councils should “rip up asphalt” to build community gardens so young people can grow vegetables, a co-founder of the Eden Project has said.

Tim Smit, who opened the giant biomes in Cornwall in 2000, has designed an “edimental” garden for the Chelsea flower show with the landscape designers Harry Holding and Alex Michaelis. The concept behind it is that plants such as cabbages and strawberries are beautiful but edible and should be placed alongside traditional bedding plants.

He hopes the garden, which will be exhibited at the show next week, will inspire people to grow fruit and vegetables at home as well as offer a template to organisations such as local councils.

Smit said: “When you look at towns, you realise you could dig up a lot of the asphalt and put up a lot of large growing boxes all over the place.” He believed this would encourage people to eat more vegetables and pave the way for farmers’ markets in town centres.

As well as launching the Eden Project, Smit restored Cornwall’s Lost Gardens of Heligan, home to 300 heritage varieties of edible plants. He has been exploring varieties of fruit and vegetables that were common before commercialisation of crops.

Many are “on the verge of extinction”, he said, as they have been deprioritised in favour of species with higher yields or more resistant to disease. Smit claims to have grown a traditional variety of strawberry that “if you crush one across the top of your palate and let the juice run over your tongue, you’ll never forget”.

The Eden Project, which turned a sterile clay pit into a garden containing plants from all over the world under two huge geodesic biomes, is estimated to have injected almost £2bn into the Cornish economy. There are 8 hectares (20 acres) of outdoor gardens containing art and seasonal displays, and the attraction has had 25 million visitors since it opened.

He once signed a letter of support for the former Green party leader Caroline Lucas, and said he was “thrilled” to see how well the party was doing with Zack Polanski at the helm. “All our life, voting Green was a wasted vote, and it’s very interesting to see how many people in the country do share green values,” he said.

Smit hopes the Chelsea flower show garden can inspire young people to care about the outdoors, and particularly plants. “I hope they get interested and through understanding they might start a garden club or get an allotment. I wish more young people had access to land,” he said.

“The degree to which we, as humans, have been denatured by not having access to land is extraordinary. One of the things which fascinates me is there is a movement of young people who want access to land to grow things, not just because they want to grow and eat things but because they want other people to as well. It’s a big movement and getting hold of land is a nightmare for young people.”

Smit hopes the “edimental” garden could help end the stereotype that gardening is “twee” and unimportant. “Gardens and gardening are often completely diminished in their importance as it is seen as a lifestyle choice. It’s seen as middle class and twee but that’s rubbish; it is a really fundamental and life-changing thing,” he said.

After Chelsea, the garden will be permanently relocated to Eden Project Morecambe, becoming part of a 1.5-acre community space for learning, gathering and stewardship.