Across the endless plain drifted the haunting, reedy sound of Andean flute music as a young boy played to a herd of alpacas. On the station platform stands an old man with one tooth. He smiles benevolently and jangles a tray of brass rings hopefully in my direction. They aren't exactly Cartier quality. There is more gold in the teeth of the Ladies in colourful skirts who toss beautiful woven rugs in through any open windows for inspection. Ahh, now these wouldn't look out of place in a peasant-chic inspired New York penthouse.

We've stop at a remote station on the 'Alti Plano' (High Plains) of Peru. The air is thin and cold. At around 13000 dizzy feet (4,000 metres) above sea level the tops of the Andes mountains look like tiny hillocks forming a scalloped edge to the plains. Only the Omo-white snow on their peaks gives the game away.

The train across the top of the Andes takes 12 hours. That's on a good day when the driver's had lunch, the engine can take the strain and there aren't any llamas on the track.

Cuzco itself is the only place I've ever flown to where the plane took off and never seemed to come down again. The city is built at cruising altitude, more than twice as high as Kathmandu in the Nepalese Himalayas and way above any ski village in the European Alps. It's the kind of place where luxury hotels have oxygen canisters on hand just in case guests need a quick blast.

To help people adapt coca tea is poured by many smaller, less luxe, hotels as soon as guests arrive in Cuzco, often with the freshly picked green leaves still floating around in the cup. Cocaine is refined from the coca leaf and the locals chew it for energy, a wad of charcoal gum lodged in the side of their mouth to release the narcotic. However, you'd have to drink buckets of tea to feel the effect. Caffeine is probably stronger. A greater jolt to the system is probably the sugar content in the sickly green Inca Kola, the nation's answer to Pepsi. It tastes like fizzy bubblegum.

Just remember as you try to acclimatize that in this rarefied mountain air the Inca civilisation once built its cities in the sky. The remains of their smooth-walled forts and mysterious citadels orbit Cuzco, city of the sun, once the capital of the Inca empire. The Incas flourished for 500 years. Then the conquering Spanish, greedy with gold fever destroyed the temples, melted down the precious metal statues and built their own elegant city on the ravaged foundations.

You can still see how the pink-washed Spanish houses are stacked on top of the original Inca walls like layer cake, then iced with lacy, Mediterranean-style balconies.

Yet to the people of the 'Alti Plano', Cuzco and its gourmet restaurants are the lowlands - a metropolis as massive and racy as New York. Its history hardly affects them. Still speaking the old Inca language they live so high that the rest of the world has simply passed them by. "Above 13000 feet (4,000 metres) there is no politics and no borders", I was told.

You can see the history of the culture in the traditional costumes the old women still wear. It is as if everyone were on their way to the Mad Hatter's tea party. The women have hooped skirts like mini-crinolines with Edwardian bowler hats. They look like Alfred Tenniel's illustrations of the Red Queen in Alice Through The Looking Glass. The men favour Dick Tracy trilbys. This isn't best-dressing, this is every day, let's-weed-the-potato-patch, garb. You see it everywhere.

At Pisac market, more than 18 miles (30 kilometres) from Cuzco, the women sit cross-legged in the dirt like rows of wilting peonies bartering their produce amid the tourists. Their multi-coloured, multi-layered petticoats fan around them like petals. In the muddy yard of an adobe house by the railway track a woman feeds her pigs while dressed in a bright scarlet bowler and a turquoise satin cut-off crinoline. In the far distance a dot of vivid pink moves across the windswept high plains.

Every hat tells a story. Bowlers are worn by the people of the highlands, the white straw top hats by those from the lowlands ("low" being a relative term). Different colours denote the tribe. A hat rammed squarely on the head means the woman is married. If it is worn decked with flowers or on the side of the head means "available". Although I did see a number of old ladies, their faces baked prune-like by the sun, who wore their hats at a suspiciously jaunty angle. Perhaps the rarefied air had affected their memory.

From Cuzco you can hope aboard yet another luxury train, the blue and gold Hiram Bingham to take you up to Machu Picchu. The train is named after the European explorer who discovered the remains of theInca citadelin 1911. It is run by Orient Express hotels and the ultimate treat at the end of the journey is to stay overnight at the five star Belmond  Machu Picchu Sanctuary Lodge , also run by Orient- Express hotels. Its orchid scented gardens sit right next the citadel and from its windows you can see the moon rise over the ruins - but that's another story.