Jenny Gilbert discovers the Aeolian islands, a secret even to Italians

Odysseus has a lot to answer for. The story goes that the Greek adventurer, pottering about the Mediterranean on his odyssey, was presented with a gift by Aeolus, ruler of the winds. The gift was a sackful of breezes to help him on his return journey. But Odysseus's crew, eager to know what was inside, peeped into the sack and accidentally let them out. They've been howling round the Aeolian Islands ever since.

Odysseus has a lot to answer for. The story goes that the Greek adventurer, pottering about the Mediterranean on his odyssey, was presented with a gift by Aeolus, ruler of the winds. The gift was a sackful of breezes to help him on his return journey. But Odysseus's crew, eager to know what was inside, peeped into the sack and accidentally let them out. They've been howling round the Aeolian Islands ever since.

Tempestuous winter weather is sometimes cited as the reason for the emptiness of this otherwise idyllic archipelago in the southern Mediterranean, just north of Sicily. A more common response is a typical Italian shrug - there's no good reason for anyone to live there: few towns, barely any farming, and scant natural resources beyond an abundance of obsidian, a hard, glass-like volcanic rock used in Roman times to make cutting tools. There are very good reasons, however, to spend a short time there in spring, summer or early autumn - not least the fact that hardly any British tourists will be doing the same as you.

There are seven inhabited islands, each with a distinct identity, and you could spend a dreamy fortnight visiting them all - taking in a spot of hydrotherapy in the sulphurous mudbaths of Vulcano; marvelling at the natural fireworks above the volcanic crater of Stromboli (it throws up sparks and flaming rock every 20 minutes or so, but they're only visible at night); or simply soaking up the chic exclusivity of Panarea, the smallest island at just 3km by 1.5km, which boasts the holiday villa of Giorgio Armani.

Having only a few days to spare at the tail-end of a Sicilian holiday, we decided to explore just one: the sleepy island of Salina, whose twin extinct volcanoes give it the shape and form of a splendid pair of pointy breasts rising out of the sea.

Salina is unique among the Aeolians for its greenery. Even the August scirocco - the scorching wind that blows from the Sahara - fails to brown the thick scrub that covers its steep and rocky slopes. It also spares the island's only exports: exotic violet-flowered capers, and a sweet, sulphurous-tasting, honey-coloured wine that is made from the malvasia grape.

Salina's turquoise waters are among the cleanest you'll find anywhere. Sandy beaches are sparse and the ones there are tend to be black, being volcanic. But renting a boat - easily done at any of the island's harbours - gives access to any number of hidden coves, caves and limpid snorkelling pools. Even the main beach at Malfa, the biggest of the island's four settlements, is empty by most standards.

Scrambling down a hewn pathway bordered by flowering pinks and wild rock roses, and arriving in a natural rocky bay picturesquely backed by ruined fisherman's huts, you could be in some Cornish cove circa 1950 - except that the sun is still hot in November, and rather more reliable.

The village of Malfa also offers your widest choice of accommodation - anything from cheap and cheerful apartments to a couple of comfortable hotels. The finest of these is the Signum, whose surprisingly low off-season rates belie its exquisite style. The owner, Clara Rametta, was born on the island, migrated to mainland Italy to qualify as a psychiatrist and pursue a love of interior design, then returned with her husband, a chef, to restore this complex of traditional Salinese buildings with the most discerning eye.

A series of low, flat-roofed, whitewashed structures set in semi-tropical garden, each bedroom is unique inside and out. One will have its own secluded terrace shrouded in plumbago and oleander, another a panoramic outlook over the quiet rooftops of Malfa, another a balcony view of the bay, so blue you have to pinch yourself to believe it.

The Signum's restaurant operates more like a private dining-room: you must tell the chef at breakfast what you'd like for dinner, so that he can source the best local produce. Salina specialities include ricciola, a rich, white-fleshed fish resembling swordfish; sweet, tiny prawns known as gamberetti, and any number of dishes flavoured with capers.

As for pudding, you can do no better than to stagger down to a local bar and order up a slushy ice granita - one of the last vestiges of Sicilian rule of the islands. Imagine slurping on prickly-pear granita, or mulberry, or almond milk, or fig. If paradise has a flavour, this is it.

Getting thereNo direct flights, but the islands can be reached from ports on mainland Italy or Sicily, including Naples and Palermo, which do have direct flights from the UK.

Getting aroundCheap bus, or hire mopeds or "scootcars" (like an open-topped bubble-car for two).

AccommodationOff-season on the Aeolians, cheap, comfortable B&Bs abound with no need to book. On Salina, try Hotel Signum (tel: 00 39 09 09 84 42 22).

Further informationThe Aeolian Tourist Office: 00 39 9880 095.