When I told people I was going to the Faroes, most responded quizzically – “Where’s that exactly?” Someone guessed Egypt (pharaoh), another Portugal (Faro). I wasn’t totally sure myself until I started planning the trip – lured by photos of the dramatic landscape.

In fact, the archipelago of 18 islands, which though self-governed belongs to the Kingdom of Denmark, is equidistant between Iceland, Norway and Scotland. It’s so far north that in peak summer (the best time to go) the islands get 19 hours of sunlight a day – take an eye mask – and temperatures rarely top 13 degrees. It’s a four-seasons-in-one-day place, so warm layers and a waterproof are essential.

Yet as remote as the Faroe Islands may be, they’re remarkably easy to get to – an hour’s flight from Edinburgh or a connecting flight via Copenhagen (making it the perfect twin-centre holiday) – and like their Nordic neighbours, the Faroese seem to have an effortless sense of style. Their most famous export to many will be the chunky snowflake knit worn by detective Sarah Lund in The Killing – made by Gudrun & Gudrun and now stocked in Harvey Nichols and Selfridges.

On our first morning we meet the brand’s designer Gudrun Ludvig in their shop, in the Faroese capital of Tórshavn. With a thick blonde fringe and covetable cableknit, she explains how she marries international trends with Faroese tradition, mixing organic fabrics (mainly wool from the islands’ many sheep) with new cuts and colours.

This balance of tradition and innovation is everywhere in the Faroe Islands. In Tórshavn’s old town, Reyn, grass-roofed wooden dwellings – some transformed into wonderful low-ceilinged restaurants (try the salt cod at Barbara Fish House and the rack of lamb at Aarstova) – are a short walk from leading sushi restaurant Etika, cosy coffee shop Paname and cool Hawaiian bar Sirkus. Record shop Tutl has a specialist Faroese section – music is huge here – while down at the harbour, design store Østrøm sells handmade jewellery, quirky fashion and sheepskin stools.

Up the road at the National Gallery, you can wander between ancient tapestries of the island’s birdlife and Tróndur Patursson’s vertigo-inducing installation of a shipping container covered entirely in mirrors.

But if, like me, you were lured here by the landscape, you’ll be chomping at the bit to get out in it. Helpfully, that’s not difficult. Quiet roads and sea tunnels mean driving around – and between – the main islands of Streymoy, Eysturoy and Vágar is easy, and most journeys won’t take more than an hour from Tórshavn (though do book ahead as there are a limited number of cars – the same applies to hotels and restaurants: this isn’t a holiday you can wing).

However, if you want to explore the more far-flung islands, the state-subsidised helicopter taxis (flights from as little as £14) are a much quicker – and more glamorous – option. With helicopters grounded by the fog that often drapes the uplands in summer, we drive one of the ‘Buttercup’ routes an hour north from Tórshavn, gawping at the lushly dramatic scenery (even the small prison, perched above a lake, looks like a superbly situated hotel).

The village of Saksun sums up the landscape perfectly: at the foot of this grass-roofed hamlet, a tiny church sits amid impossibly green meadows sprinkled with sheep, while, on either side, craggy mountains plunge into a lagoon formed by the fjord. At low tide you can walk round the headland to what locals call the ‘hidden beach’.

That evening we eat at the home of farmers Anna and Oli in Velbastaour – an experience called heimablídni (‘home hospitality’) available across the islands (see visitfaroeislands.com). I’m not sure what I expected, but it wasn’t a house worthy of its own Pinterest board (complete with hot tub and stunning views of neighbouring island Koltur) and a five-course meal to put most supper clubs to shame.

Between serving us dishes of bacalao (salt cod), their own lamb, and rhubarb (one of the few things grown on the islands) ice cream, plus locally brewed Okkara beer, Anna and Oli chat to us about their life here. The Faroese – population: 50,000 – claim to be the happiest people in the world* and watching the sun turn the sky into coral swirls, I’m not surprised.

Perhaps the only thing the islands are missing is luxury accommodation – Hotel Føroyar in Tórshavn is perhaps the closest you get to it. But you come to the Faroes for adventure, not luxury, and there’s plenty of that to be found.

After a walk around Lake Sørvágsvatn on the island of Vágar the next morning, the Faroe Islands have worked their magic on me, but there is one thing I still haven’t seen: a puffin. For this, you need to take a boat. The bird cliffs of Vestmanna are a hot spot, and boats depart regularly (£35 for two hours; puffin.fo), but we see far more on a trip organised by Kristian Blak, the godfather of Faroese music (£53; June to August; nordlysid.com).

A 20-minute bus ride from Tórshavn takes us to an old schooner and the island of Hestur, where we climb aboard speedboats and head into a grotto. Here we’re serenaded by Blak, perched on a cliff in the cave with his Yamaha keyboard and ancient Faroese pipes.

As the music reverberates round the cave, it’s strangely mesmerising. Perhaps the puffins like it too, as on our way back we are greeted by a colony in the water, some ducking at the sight of us while others take to the skies, flapping madly over our boat. I couldn’t resist buying a keyring of these cute, comical creatures. Tucked in my suitcase alongside a pair of Gudrun & Gudrun socks, it’s a neat summary of these wild, yet incredibly chic, islands.

Flights from London to the Faroe Islands via Copenhagen start from £197 return with Scandinavian Airlines; flysas.co.uk. For more information on the Faroe Islands, see visitfaroeislands.com