Life on the most northerly inhabited island in Britain can be very tough indeed. On Unst the winters are harsh, and the winds brutal and relentless, regularly sweeping across the treeless landscape at more than 100mph.

But Unst is the island chosen by a retired couple from Wiltshire to build one of the world's greenest houses - a "zero carbon" home powered entirely by the wind and the sun. It sits on the same latitude as southern Greenland, but will soon boast lemon trees, grapevines and green pepper plants in its greenhouse, an electric car powered by the wind, and floors heated by drawing warmth from the air.

The three-bedroom home designed by Michael and Dorothy Rea, near the shoreline of a secluded bay, has become a test bed for living "off-grid": generating all their power from renewable sources, growing most of their food at home, and running a car without a petrol station.

Their home - built for just over £210,000 from an off-the-shelf timber framed house - has quietly become famous. The Scottish executive in Edinburgh is using it as a benchmark for new sustainable house-building rules; officials in the prime minister's office watch its progress and Chinese officials are studying its innovative technologies for a new 5,000-home eco-town in Guangzhou, in southern China.

Last year, the Reas learned that their website - zerocarbonhouse.com - was the fourth most popular site worldwide on Google. Michael Rea is often up at 5am answering emails from PhD students, green activists and even Canadian senators.

The Reas believe their home is the first of its kind. "If we can do this here, anyone can do it anywhere," said Dorothy, a former headteacher. "It's just an ordinary house. It could be in Edinburgh; it could be in Chigwell."

"It's definitely significant," said Duncan Price, a director of one of the world's largest green energy consultancies, ESD, and an advisor to the Reas. "What's very special is they're trying to address the carbon impact of their whole lifestyle. It's a microcosm of how the world would be in a carbon-constrained future."

It is one of several pioneering off-grid projects in remote areas of Scotland, where communities such as the islanders on Eigg in the inner Hebrides and another living on Scoraig, a remote peninsula near Ullapool in north-west Scotland, have developed their own independent green power sources.

Around 80 people living on Scoraig, which is only accessible by boat or with a five-mile trek overland, power their homes and businesses chiefly using small hand-made wind turbines designed by local resident Hugh Piggott, a guru of self-sufficient off-grid living. Solar panels and diesel generators supplement the turbines.

In February, the islanders of Eigg, just south of Skye, switched on the UK's first independent "green grid". It provides power to all the 45 homes and 20 businesses by combining electricity from wind turbines, solar panels and two small hydro-electric dams into a single supply. For the first time, islanders can run fridges, electric kettles, satellite TVs and computers without using unreliable oil-powered generators.

Forced by their isolation to become self-sufficient, many observers believe these communities prove that micro-generation and home energy schemes are viable UK-wide. Nick Rosen, author of How to Live Off-Grid, a handbook on off-grid communities, said: "It doesn't mean we should all live like Scoraig but we should be fostering communities like it all over the place. It increases the self-reliance of our society overall, in the event of sudden energy price hikes, the Russians cut off the gas or strikes in the oil industry."

The Reas are not naive about the severity of Shetland's weather or the scale of the challenge. They erected the timber frame for their new home during a gale in November 2006; the strongest gusts threw heavy roof sections through the air, smashing one to the ground.

Shetland, the Reas note wryly, has the strongest and most reliable winds of any inhabited part of the world, closely followed by the Falkland islands. But then they have striking views over a south-facing bay across to the low-slung, mottled green islands of Uyea, Fetlar and Yell. In midsummer, the temperature can hit 30C and the sun never sets.

"I could foresee the time when energy would be very, very expensive," Michael Rea said. "But at first what we were doing was viewed as the black arts, but we weren't cranks. We were ordinary people."

Although they describe their home as normal, it will use advanced low-carbon technologies, many of which are being fitted this summer. With help from Dundee University and Duchy College in Cornwall, they are building a greenhouse which uses hydroponics where their vegetables, fruit and herbs will be grown in a liquid with specially controlled lighting to create artificial "seasons". The University of Delaware is refitting a Toyota Yaris car with an electric engine.

Dogged and single-minded, Michael Rea has cajoled builders, banks and even the window firm Velux into sponsoring the project. Eventually, the house will be lit by very low energy LED lights, the greenhouse will use electricity from its own wind turbine and the chief source of heating will be a heat pump which draws warmth from the air into an under-floor system.

"I have been waiting 24 years for this house to be built," said Dorothy, 65. "But it's just a standard house, an honest house, nothing fancy. It's a serious project in renewable design and energy efficiency, an experiment in joined-up technology, but it's also a house we intend to grow old in."

Explainer: How heat is harnessed

The house is very heavily insulated and its under-floor heating uses warmth drawn from the outside air and stored in a giant "water battery". Heat inside the house is captured by a ventilation system and reused. Rainwater is harvested for toilets and the washing machine. Large windows capture warmth from the sun.

Power for dishwasher, cooker, toaster, fridge, computers and lights comes from a wind turbine, which charges fuel cells able to store power for four days. The house's LED lights will use the same power as one 100W bulb.

The greenhouse will have its own wind turbine. Plants will grow in high-nutrient hydroponic liquids, with special LED lights to create artificial seasons and daylight. A converted battery-powered Toyota Yaris will be charged from the fuel cells.