There's a disarming aspect to the Faroese relationship with nature that's illustrated at the country's diminutive Natural History Museum, situated in the equally diminutive capital, Tórshavn. Here, amid the stuffed birds, papier-mâché fish and dual language displays on the country's glacial geology is a tiny gift shop selling a broad range of the stock tourist souvenir – puffin paraphernalia. Glove puppets, key-rings, fluffy toys, salt and pepper shakers and fridge magnets form most of the shop's stock, but next to them, a gaily coloured postcard on a rack shows a man striding across a stunning landscape holding a shotgun, some hundred dead puffins slung over his shoulder with the kind of nonchalance Alexa Chung brings to her latest Mulberry bag. With its barbaric overtones, the image of so many of these surprisingly small, dead birds is a shocking one, made more so by the fact that many people here are at pains to move the country beyond the idea of puffins and pilot whale being slain for food and sport, the things the country's most often associated with. Well, those, and a certain jumper.
There can be few fans of phenomenally popular Danish TV series 'The Killing' unaware that the iconic knitwear worn by gutsy detective Sarah Lund was made in the Faroes, using wool from some of the 72,000 shaggy-haired sheep that roam the wild, windswept archipelago. Eighteen islands make up the Faroes, and while they're not all inhabited by humans (two are are only inhabited by one family each), the sheep are everywhere; scuttling out of the way of traffic on the roads, grazing on the grassy verges of tiny beaches, or perched precariously on the inches-wide ledges of sheer cliffs that soar vertically out of the sea and slope gently away into basin valleys on the other. In Faroese, the country's name, Føroyar, is made up of the word 'før', meaning sheep, and 'oyar', meaning island.
It may all feel untamed, empty and like you've reached the end of the Earth, but getting around the islands is easy, thanks to numerous bridges, undersea tunnels and an impressive range of ferries: a huge liner runs daily between Tórshavn and the southernmost island of Suðuroy, while a tiny, five-car one takes walkers from Eysturoy to Kalsoy, where on clear days spectacular walks in the northern half of the long, thin volcanic island offer views of five islands. It's walking that most people come here for, but thanks to the tiny numbers of visitors – around 500 hotel beds were used by fewer than 1,400 British tourists last year – you don't have to go far to find trails where the only other living things you'll see are sheep and a giddying array of birds, leaving you to quietly commune with nature and enjoy views that are some of the best you'll get less than two and a half hours from London.
Even in the capital, it's easy to to pick up the trail that takes you to Kirkjubøur, the ancient spiritual heart of the islands and home to the ruins of St Magnus’s Cathedral and Roykstovan, claimed to be the world’s oldest continually inhabited wooden house. The views of neighbouring islands Koltur, Hestur and Sandoy as you walk are stunning, and you don't even have to walk back; four buses run between Kirkjubøur and Torshavn, and like all the city buses, they're free, and have free wifi.
Tórshavn itself is a good base for visitors, not least because of its decent selection of bars, most of which are huddled around the picturesque port - try Café Natúr (Áarvegur 7, +298 312625), Kaffe Vagsbotn and Kaffi Husid (Bryggjubakki 14, +298 358787). Elsewhere in the town, there's also an art gallery that holds touring exhibitions and houses an enjoyable collection of Faroese fine art, the winsome old town area of Tinganes (where most of the houses are still capped with traditional grass roofs) and decent shopping opportunities at fashion knitwear shop Guðrun & Guðrun (Dalagøta 12, +45 29 617077), Siri (Dr. Jacobsensgøta 18, +298 316610) which stocks designs by the country's most famous designer and H&M collaborator Johanna Steinum, and Faroese glassware gallery Rabarbuglas (Tvørgøta 16, +298 224410). One of the country's two cinemas is here, too.
If you're a serious walker, Tórshavn is good for its access to all the southern islands, but a good second base for the tallest, most rugged and sheer cliff faces of the northern islands is Klaksvik on Borðoy. This one-time capital city is a friendly, laid-back place to visit in its own right, not least for its church, designed by Danish architect Peter Koch around a 1901 fresco by celebrated Scandinavian painter Joakim Skovgaard. Its baptismal font, featuring a 4,000 year old sacrificial granite bowl, is moving, as is the eight-ore boat hanging from the Norse-style rafters, once you've read its history in the useful dual-language booklet about the church. But best of all, Klaksvik is within easy reach of the Faroes at their most remote and beautiful.
The Faroese are desperate to find ways of keeping their young people from leaving to study in Denmark (of which it classes itself a 'self-governing community'). But in fact, the country already has what it needs to get its youth back; it just needs to persuade its modern youngsters that theirs is not a country of pilot whale driving and puffin-munching, but a spectacular country where nature informs and impacts on every aspect of modern life, from the expressive landscapes in the national art gallery to the fashion, cuisine, and music. Nightlife, too: on Midsummer's day, the country's hardier party animals head for Sornfelli, mountain site of a former Nato radar base, to drink and party while watching the sun set on the summit's eastern side, before clambering over the knife-edge ridge to watch it rise again an hour later on the western side. I met one of these adventurous revellers; a gothy looking girl at a bus stop. Curious to know what I was doing there, we got chatting and she asked me which islands I'd been to, before insisting that without going to the northern islands of Vidoy, Svinoy and Fugloy, I hadn't seen the Faroes at all. She had studied abroad and clearly needed no enticements to return to her country, and spurred by her enthusiasm for what I had missed, neither do I.
The low-slung modernist-style Hotel Føroyar (Oyggjarvegur 45, +298317500) blends into the surrounding green hills in a distinctly Teletubbies-ish way. Doubles from £98.
At the Hotel Føroyar restaurant, Koks, chef Leif Sørensen specialises in creating extraordinary modern cuisine using traditional local ingredients such as air-dried Faroes cod and lamb, and offers a fantastic selection of tasting menus. In town, traditional Faroese restaurant Aarstova (Gongin 1, +298 333000) is housed in a series of characterful rooms. Or try Ingongd (Vaglið 5, +298 317405) for Faroese fiskur and kipsi – fish and chips.
Every day during the summer, vintage schooner the Norðlýsið sets sails from Torshavn to the nearby island of Nolsoy and along the coast, where well-known Faroese musicians play live concerts in the sea caves. Tickets cost £48 per person.
Atlantic Airways operates flights from London Gatwick to Vágar airport twice weekly in summer; returns from £263. Sunvil Discovery offers three and four-day packages and longer breaks in the Faroe Islands. Gatwick Express runs between Victoria station and Gatwick Airport every 15 minutes with a journey time of 30 minutes. Tickets from £16.85.