In this world there are some things only seagulls understand. One of them is Milos. For most of us, its a mountainous crumb of golden limestone, rising up out of the Aegean.

Sprout wings, however, and a glorious, secret landscape appears. You can now see fjords and blowholes, and the coves become a luminous peacock-blue. In the wind-sculpted cliffs, there are arches and organ-pipes, and the valleys turn turquoise as they find the sea and tumble off into the deep. Then a monastery appears, way out on a knob of rock. Now that, you say, is proper prayer.

Ill never forget being a bird or, rather, my ride in a Cessna 182-F. The pilot, Kostas, seemed to know every bay, and wed whirr along at 35 beaches an hour. Sometimes hed swoop down on his favourite places: a Roman amphitheatre perhaps, a Venetian fort or an island of goats. Occasionally, the rock itself would open up, and sulphur mines would appear, like giant staircases descending into the Earth. At the far end of the island we circled a magnificent egg-shaped headland, mounted with a tiny sprig of rust.

An anti-aircraft gun, said Kostas, left by the Germans.

Flying around the Cyclades isnt just about birds-eye views. People have been sailing from crumb-to-crumb for more than 8,000 years, and even Pliny mentions the sulphur.

In the 1850s, an entire French fleet filed into Milos harbour as they hopped their way to Crimea. These inter-island leaps are still fun, of course, but ships can take time, and the ferries keep curious hours.

The other option is to fly. Even this can be a heart-sinking thought for those weary of queues and lounges. Thats why Aria Hotels has devised a new service, to get their guests around. For the price of a scheduled flight, you go whenever you want. They just ring up Kostas, and the Cessna appears. Its your own little airline, at your beck and call. The Uber of the gods, I suggested.

Kostas smiled although I now realise that G-IART isnt simply a taxi. Built in 1963, every bit of her is loved, and shes a little jewel of engineering. Amid all that retro and chrome, it sometimes felt as if we were flying along in a Wurlitzer (except that all the windows were filled with islands). Even her buzz sounded well-machined: more mosquito whine than cackle of birds. In just 50 minutes she can hop the Aegean and be back in Athens.

I spent the night on Milos before flying on. Naturally, this being a tale of air and propellers, I stayed in a windmill. Its old walls were so thick there was only space for three cosy rooms.

Every window looked out to sea, and the front-door key weighed almost a pound. But the miller would have been puzzled by the transformation of his attic, and the arrival of flat screens and Egyptian cotton. Only at breakfast did real life intrude, when the goats appeared like a river of bells.

That morning, I took a walk through the landscape Id known from above. Milos can be not only enchanting but also surprisingly sheer. After the fort and a field full of cats, I arrived in Plaka, where the churchyard falls hundreds of feet on to the plains below.

My own little hill was called Trypiti, or The Hollows, and was honeycombed with tombs. In 1820, a ploughman had slithered into one of these holes, only to emerge with the Venus de Milo. Although shes now in the Louvre, it was up here that shed perfected those curves.

On the way to the airstrip, I stopped for a swim at Firopotamos. My taxi-driver chatted about the old silver mines, and the annual dynamite-throwing competition. But Firopotamos, he said, is the softest place in the world, and the people live in caves. This made more sense down in the inlet, surrounded by silence and by fishing lofts deeply embedded in the rock.

Id have happily paddled around all day if my plane hadnt had a passenger to catch. Id arranged with Kostas to leave after lunch. Like Icaruss father, we never flew too high. At 2,500ft, our planet looks satisfyingly spherical and yet you can still peer down on peoples lives.

We began with Kimolos, which produces the worlds cimolite, and has 80 churches for 600 souls. Then we were over open water, trilling past Folegandros, and little silvery Sikinos. I was just thinking how idyllic it all looked when a great black disc appeared on the horizon: Santorini.

No wonder the ancients called it Devils Island. Close-up, the caldera was prettier but no less forbidding. The whole of central London would fit inside its submerged crater, and the remnants of its rim are marbled in pinks and oranges, and rise the height of The Shard.

Circling around it, I suddenly felt as though I understood what had happened. After millions of years spent blasting Greece with dust and pumice, in about 1628BC, the great volcano had imploded. The ensuing tsunami would wipe out much of Crete, bringing Minoan civilisation to an abrupt end.

The radio crackled, and we had permission to enter the crater. This is how a fly must feel as it buzzes through our world. Amid the dizzying perspectives I spotted a cruise ship the size of a nit, and Nea Kameni, a new volcano, nosing up from the depths.

Then we were soaring over the rim, and down the islands outer slopes. Even here, Santorini can look magnificently post-apocalyptic. Everythings layered in ash; there are no rivers or ponds; the farms look like forts, and it all ends in a band of black sand and wild surf.

I spent the rest of the week picking my way through this fantastical scenery. Although arc-shaped Santorini is only the size of Guernsey, much of it is vertical. I dont think I ever lost that feeling of being airborne.

It helped that my exquisite little hyposkapha or cave-house was built right on the lip of the caldera, with a drop of more than 970ft into the sea below. It was a view full of drama and shipping (in 2007, one of the liners had sunk, leaving nothing but a ring of buoys). I even caught one last glimpse of Kostas, as he flew along the cliffs and out of the crater.

Everyone lives in caves up here, in varying states of boutique-ification. Mine had a Jacuzzi but others had swimming pools and gardens dangling over the void.

Some of my neighbours were Japanese, and Id often see them, wandering around in their wedding dresses. There were also a few troglodytic locals.

My landlord told me that many had fled after the 1956 earthquake but now The Crisis was driving them home. Life is miserable in Athens, he shrugged, but not here. Our economy is different.

From my cave, I set out in all directions. To the north, the cliff path led all the way round the rim, five miles to Oia. Along the way, I met lizards, hawks, a greengrocer with a handcart, and a man selling coffee from his moped. Oia, meanwhile, has risen from its rubble, and is now a spectacle of plate-glass and colours. You can even walk home in a pair of new Jimmy Choos.

Walking in the other direction, I came to Fira. Exuberant and terraced, it was like a theatre perched on the rim.

Every day, the towns donkeys would haul an audience into place, up 587 steps from the cruise ships below. Everything was sold with a flourish. Santorini, ran one ad, The island in the bowels of the Earth.

On my last morning, I boarded a catamaran and sailed around the crater. From down here, Fira looked minute. It was a day of colours: green sand, white stacks, scarlet cliffs, and gorgeous submarine blues. At one point, we clambered over some charred black lava, which had only emerged from the sea in 1866.

The water here was orange and fizzy, and it was like swimming around in mulled Lucozade. I asked the skipper if hed been born here, in this fabulous newly-minted world. No, he said, Santorini had no maternity hospital then. I was born on the ferry.

I was sorry to be tearing myself away, and would regret not calling Kostas. Instead, I took the hydrofoil, 4 hours back to Piraeus. As we pulled out of the crater, I took one last look at Nea Kameni, now the most active vent in the south Aegean. I remember thinking how utterly awesome it had looked from the air, and how harmless it looked from the sea. After that, I was shown to my seat, and saw nothing at all but the reel-to-reel repertoire of Mr Bean.

John Gimlette travelled as a guest of Aria Hotels (0030 210 8996056; ariahotels.gr). Its Fly Me to Aria service (ariahotels.gr/en/pages/fly_me_to_aria) allows guests to travel by air between Arias hotels or villas, wherever there is an airport. The Cessna used can accommodate three passengers, and prices are broadly equivalent to those of scheduled flights (rates supplied on request). The ferry from Piraeus to Milos costs 39 per person, and a hydrofoil from Santorini back to Piraeus costs 76 per person (directferries.co.uk)

Aera Milos, Milos: This old stone windmill has been stylishly restored by the Aria Hotels group, with polished concrete floors and designer furnishings. Although there is no kitchen, there are plenty of local restaurants (from 160 (140) per night for two people).

Caipirinha Residence, Santorini: With a balcony on the lip of the caldera, this is the kind of place you could spend all week, just gawping. The traditional one-bedroom residence has been given a new lease of life by the Aria group, and has an interior spa and an outdoor whirlpool spa, both heated, among its facilities (from 450 per night for two people).

A half-day catamaran trip around the caldera in Santorini costs around 155, including drinks, snorkelling equipment and dinner. The site of Akrotiri, the city destroyed by the volcano circa 1628BC, is reached by bus from Fira (2); entrance costs 12. Akrotiris treasures are displayed at Firas Museum of Prehistoric Thera (entry 6). Boat trips to the volcano in the centre of the crater, Nea Kameni, cost 20, or around 150 for a day-trip by catamaran. Its another 2 to enter the national park.

9 Telegraph expert rating

9 Telegraph expert rating

From 1,618 inc. tax

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The hotel that offers guests their own plane to explore the Greek islands - Telegraph.co.uk