Against all the evidence, I had arrived thinking of the Aeolian Islands as an activity holiday. I was set up for island-hopping, for boaty adventures. Just because there was a hammock on the terrace and Diana Krall on the CD player, there was no reason to surrender to another glass of prosecco and the cosmic appeal of the afternoon nap. I wanted to climb Stromboli. I wanted to gaze into the mouth of the volcano. I wanted a glimpse of the earth’s core.

But midway through the week, a strange thing happened. It rained. The skies opened and I watched the Italians scurry between the alimentari and the macelleria, with newspapers on their heads. An air of resignation seeped into the town. People became restrained, subdued. For an afternoon, in the rain, the Italians became a bit like us.

Had the bad weather continued, they would presumably have turned to loutishness and bad haircuts. As it was, the sun returned and so did their charm. But the winds had changed, and the winds have been a preoccupation on the Aeolians since Odysseus stopped here on his long way home. Boatmen now peered across the water, pursing their lips like London cabbies offered a fare to Deptford. ”Don’t know, mate. Looks a bit rough,” they said. Though in Sicilian, so perhaps they threw in the possibility of sleeping with fishes.

I had seen heavier seas in a fish tank. A life on the edge of the Atlantic makes Mediterranean “rough” rather unconvincing. But Italians didn’t get cool by putting themselves out. They spoke darkly of “long waves”, as if it might be the short, choppy variety they preferred, before returning to the bar for another crodino and a hand of cards with their mates. Stromboli stood across the sea beneath that kind of halo of sunlight that on religious postcards means “God”.

The Aeolians lie off the north coast of Sicily: seven picturesque islands surrounded by a scattering of rock outcrops in azure seas. Theirs is a classic Mediterranean world — elegant yachts, tiny harbours of white and pastel houses framed by pine and bougainvillea, handsome well-tanned people strolling in a myrtle-scented, cicada-droning heat, and the pervading sense that you have been a fool to spend so much of your life on Europe’s northern fringes.

Like Sicily itself, the islands were Greek long before Rome was Rome, and they share the remoteness of the best Greek islands, aloof from the world, content with their own insular existence. Though only two are still active, all the islands are volcanic. The steep craters at their centre lend them a kind of bad-boy glamour.

The Aeolians are a star turn in numerous films. Stromboli was the first, featuring in an eponymous film in the 1950s directed by Rossellini and starring Ingrid Bergman. The isolated beauty of the island made them forget themselves and the story of their off-screen romance — he was married at the time — almost overshadowed the film. More recently, Salina served as the ravishing setting for Il Postino.

I BEGAN on Salina, pre-rain, staying at Capofaro, where the villas are set among malvasia vineyards. It is an idyllic place with views across the sea towards Stromboli and Panarea. In the mornings, beautiful girls in wafty cotton served me breakfast in an elegant open-air dining room, and at night, when a lighthouse beam ghosted across the walls of my room, you could see trailing sparks from the summit of Stromboli.

Diving was off — too early in the season, apparently — so I hired a scooter and toured the island’s dizzy roads. At Pollara, on the western tip, beneath a ruined Moorish lighthouse, I followed a steep path through a cleft in the rocks to a stony but spectacular beach set against dramatic cliffs. It was a secluded and pristine spot. The water was clear as glass and deliciously warm.

Which is what makes the island of Vulcano such a mystery. In one of the most beautiful archipelagos in the Mediterranean, with the most limpid and gorgeous of seas, visitors to Vulcano queue up to sit in a stinking mud hole. I needed to check it out. Even before the ferry had docked at Vulcano I was assailed by a sulphurous rotten-egg stench.

Volcanic activity is the earth’s indigestion, a sort of gastroenteritis of the lower asthenosphere. Deep rumblings produce sudden eruptions and a series of foul smells. There is no good reason why anyone should want to sit in it. But a surprising number of people do. It is based on the old cod-liver-oil principle: whatever is most loathsome must be good for you.

Vulcano’s fanghi, as it is known, is the size of a village pond. It contains a sort of yellow volcanic soup. The pond is shallow, hardly thigh-deep, and bathers sit or squat in this foul-smelling gloop, scooping up handfuls of mud from the bottom and smearing it over their bodies. The beautiful people, normally so much a feature of the Aeolians, were notably absent. I was surrounded by elderly Italians, a handful of bemused English and a party of pasty Russians. Hopes that the experience might be lightened by a couple of babes in bikinis, possibly engaged in a little light mud-wrestling, were ill-founded.

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