British garden designer Tom Stuart-Smith made his name close to home. The winner of eight gold medals and three Best in Show awards at London’s annual Chelsea Flower Show—the Oscars of the gardening world—he has counted among his clients Queen Elizabeth II, for whom he designed a garden at Windsor Castle.

Mr. Stuart-Smith, who works out of a studio in inner London’s Clerkenwell district, has just finished a spacious walled garden in Cheshire alongside a 19th-century brick house, and a pair of enclosed garden spaces in Norfolk, near the North Sea, complemented by a wild garden between a restored 18th-century farmhouse and fields leading to a beach.

Now, he is taking his sketchpad on the road. He is designing gardens as far afield as northern Wisconsin, where he is creating a landscape for a compound belonging to members of a Midwestern industrial dynasty, and southern India, where he is working with a team of Mumbai architects to create gardens around a cluster of residential buildings in Kerala state.

Each garden he creates is different, says Mr. Stuart-Smith, but his overall approach is marked by “a strong geometrical structure” and “planting in a natural way.” That sense of structure follows his investigation into the natural and demographic history of a site. He sometimes likes to create a wild effect with plants like American grasses.

Mr. Stuart-Smith says he wants the eye to notice space and overall shapes “not whether this a pink bush or white bush.” That means his gardens tend to have “quite a bit of complexity,” he says, not “a beginning, a middle and an end.” A word he disdains in garden design is “minimalism.”

Always, a garden begins with a sketch, says the 53-year-old. “If I don’t draw something, I haven’t connected with it in a proper way,” he says. People think of planting being “the thing,” he adds, “but ordering principles are what’s most important—how you go about making a place.”

He says his ideas don’t come from gardening traditions or looking at paintings—common sources of design ideas—but rather from looking at natural landscapes and natural patterns of vegetation. He also is inspired by classical music, he says.

His urban gardens can be small, but his projects also have covered dozens of acres. At the Connaught, a luxury hotel in London’s Mayfair district, he designed a 10-by-40-foot garden with a reflective serpentine pond. In Islington, in northeast London, he designed a small residential garden presided over by eight exotic tree ferns. He planted climbing hydrangeas in the walled space that flower in the summer; the ground is covered with a deciduous grass that becomes rusty-brown in autumn.

His budgets start at about $300,000 and can reach $7.6 million. He has benefitted from the professionalization of garden design in the U.K, where amateur gardening otherwise is a national passion. Until recently, he says, the British were loath to hand over control to an outside garden designer. Knowing how to lay out a garden was thought of as “part of the equipment you’re born with,” he says, “like knowing the difference between burgundy and claret.”

Mr. Stuart-Smith grew up in Hertfordshire, outside London, on a 250-acre estate built around a Queen Anne house, where he picked up gardening early. “I realized that gardening was something I really loved,” he says of his teenage years.

He returned home in the 1990s after doing post-graduate work in landscape architecture in Manchester, and began to design a garden on land acquired from his family. “There was nothing there when we started,” he says, just “50 acres of wheat.”

The results were featured in an article in House & Garden magazine, which led to a professional breakthrough in 1998 when German fashion designer Karl Lagerfeld, head designer at the Chanel fashion house, asked him to enter the Chelsea Flower Show with a Baroque garden design.

“It wasn’t the garden I would have designed myself,” he confesses, “but I had this amazing experience” of collaborating with Mr. Lagerfeld. It was a publicity-grabbing experience, he adds, that led to him “being pushed right out there onto the deck, as it were.”

Clients have varying expectations of Mr. Stuart-Smith, who oversees a staff of eight or nine architects and landscape architects, and shares an open-plan office with two other landscaping firms. Although clients rarely ask for departures from his designs, he has noticed that some security-conscious people “want to surround themselves with prickly plants” to ward off thieves.

“You have to talk them out of it,” he says.

The length of time spent on projects means there is often overlap. “In a typical month we might be working on 30 to 40 gardens,” he says. “I might be working on a garden for seven or eight years, or even 20 years. It’s completely up to client if they want to keep us involved.”

He thinks of his gardens as intimate creations, which are then handed to their owners to care for and perhaps to reinvent. “We’re like an adoption service,” he says of his business. “You’re giving somebody something, and you hope that they make it their own.”