“Movement is medicine.” Such is the mantra of Yeotown, a wellness resort in Madeira, the autonomous region of Portugal. The five-day program involves every possible prescription, from a near-vertical pre-breakfast trot to candlelit yoga on a platform overlooking the island’s balmy southern shore.

When the sun eventually rises over the 17th-century Quinta das Vinhas hotel, it illuminates the electric blue of hydrangea and the red of Brobdingnagian hibiscus.

Terraces of organic vines zigzag down to the ocean. The celebrated Malmsey grapes are harvested from them; they are used to make a sweet, fortified wine that was rumored to be the Founding Fathers’ favorite tipple, used to toast American independence in 1776. Jefferson ordered 3,500 bottles of it in the first year of his presidency, and Benjamin Franklin confessed he would prefer to drown in a cask of the stuff, like a fly, rather than suffer an ordinary death.

Guest rooms are located in the 17th-century Quinta das Vinhas.

But all types of nectar—including alcohol, sugar, and dairy—are prohibited on this detoxifying week of an exclusively plant-based diet. Up on our platform, our yoga teacher, the Canadian-born and Cambridge-educated Mercedes Ngoh Sieff, has a singing voice that coaxes magic out of stubborn limbs and minds. “The ground is solid beneath you, and you have no limits but the sky,” she says. Her incantations have us leaning into handstands and balancing in crow.

Along with her husband, the former London gallerist Simon Sieff, Mercedes has co-founded Yeotown. Its original location is a legendary ashram in the West Country of England; last winter, the Sieffs launched an offshoot of their signature North Devon retreat located in a charming farmhouse on a remote Atlantic island.

For its five-day retreat, Yeotown imposes a plant-based diet and prohibits alcohol, sugar, and dairy.

Exuding Bambi-esque youthful energy and good cheer, the Sieffs are the poster couple for clean living. Madeira is, they insist, Europe’s perfect alternative to Bali, with its surf breaks, outdoor lifestyle, and constant sunshine. Moreover, it is just over a three-hour flight from London, and now Azores Airlines flies direct from New York’s John F. Kennedy International Airport.

Abraham Lincoln confessed he would prefer to drown in a cask of the stuff, like a fly, rather than suffer an ordinary death.

Three times the size of Nantucket, or twice the size of the Isle of Wight, this volcanic island, punching through the Atlantic’s ocean floor, is closer to Africa than to Europe. While it’s part of the European Union, it feels like a finis terrae, the end of the earth. Even the airport runway had to be extended into the sea on elevated piers; there was no flat land available.

Many of Madeira’s beaches are accessed by boat or heart-stopping cable cars. Every day, we marched in single file across 30 miles of windswept plateau, misty laurel forest, and along ancient, man-made, irrigation channels called levadas. Above the cloud line, at 6,000 feet, we staggered up the mountain summits of Pico Ruivo and Pico do Arieiro before skipping down waterfall-studded valleys to meet the surf-raked shores.

Swimming—whether frolicking in the sea or doing laps in Yeotown Madiera’s pool—counts as exercise.

My detox cohorts included a soap-opera actress from New Orleans, the dynamo head of a U.K. television company, a well-known British radio broadcaster, an alpha-male floral architect from Holland, and a mother-cum-entrepreneur. We met as a disparate bunch of mutually suspicious strangers and competitive high achievers, but by day five we had become a surprisingly cohesive group of oversharers.

We bonded over common fantasies of Michelin-starred dinners, along with confessionals about bowel movements and lost libidos. On the same deprivation high—and after lap swimming in the chill of Seixal’s natural-seawater basin—we were photographed throwing euphoric “X” poses in our swimsuits on the pontoon.

The surf crashed, and we were sodden and goosefleshed, and yet laughing. Who could imagine that this reset on a profound cellular level on this sedate and forgotten little island of Madeira would also prove to be one of the most memorably liberating holidays of all?

Yeotown Madeira’s programs run weekly from Tuesday morning to Saturday at lunchtime; rates begin at $3,500 per person, all-inclusive

Catherine Fairweather is a travel writer for The Guardian, the Financial Times, British Vogue, and others. She is based in England’s West Country