For too long, there’s been a significant gap in my personal map of South America. I’ve covered most of it by plane, coach, ferry and horse, but never Peru and never anywhere by train.

At the start of the year, a friend was touring the country, documenting it constantly on Instagram. I found myself checking impatiently for fresh posts, newly obsessed with scenery that I still, frustratingly, had yet to see for myself.

At the same time, everywhere I looked, Peru was calling: its cuisine had taken over from pulled pork as the in-thing, and South American chef Virgilio Martínez was now the pin-up boy of international fine dining. In Soho and Shoreditch, you couldn’t move for ceviche.

I had also become fixated with the fancy new sleeper train that was running in Peru. Last year, Belmond launched the Andean Explorer, bringing plush, boutique-hotel tropes, South American handicraft and a grand piano to the rails running through the high-altitude landscape that stretches from Arequipa to Cusco.

To mark its first anniversary, Belmond added a spa car to the train, so you could be massaged while passing fields full of pretty vicuñas and llamas.

I love luxury trains with the same passion that I hate airports. In the midst of a dark London winter, it was all adding up. Before my friend had got over her jet lag, I’d splurged on a return ticket to Lima. Tourism in Peru, as I discovered when planning my journey, is getting slicker by the minute and Belmond – the brand formerly known as Orient Express – has much of it sewn up, with its own five-star hotels almost everywhere you would consider visiting.

A specialist tour operator for the country, Aracari, recently launched a tour that takes the Belmond Andean Explorer as the core experience for a broader two-week trip. You start off rebooting from jet lag by the pool at the super-chic Belmond Miraflores Park in Lima – where you periodically find yourself swimming in a cloud that’s rolled in off the sea – then fly to Cusco. You visit Machu Picchu, explore the city and landscape, then spend two nights on the sleeper train to Arequipa, going deep into the Colca Valley.

In 20 years of travel writing, this is a fortnight that went straight into my top three experiences of all time. No photograph could ever do the landscapes justice.

When I was working on my itinerary, a friend who had been to Machu Picchu recently suggested I consider skipping it. “You have to ask yourself,” he said, with raised eyebrow, “do you want to be anywhere with 2,500 people?” As it turned out, I did. I was blessed with a perfect day: blazing sunshine, dramatic ever-changing cloudscape, and a low turnout. But even in horizontal rain surrounded by hordes, the impact of this Inca summer palace, with its dreamlike terraces and vertiginous tropical mountains, wouldn’t be diminished.

On an Aracari itinerary, you spend three-and-a-half hours on the Belmond Hiram Bingham train, which is set up for lunch and pisco sours in the bar car, following a route along a cascading river to Aguas Calientes, the town at the foot of the ruins. The scenery on that trip is some of the best you’ll experience, ever, and then you hit Machu Picchu in the afternoon.

There’s not much to see in the town itself, but an overnighter at the Sumaq hotel close to the station is a must, for no better reason than you can have a bedroom with a whirlpool tub that looks out to that wild river across the street, and you can also get another stab at the ruins, and mountain climbing, first thing in the morning.

After Machu Picchu, I returned to Cusco and was taken by my Aracari guide Leo to the salt pans of Maras: a silver and clay-coloured valley with giant flooded cells used to harvest the finest quality of salt. It looked like a biblical patchwork quilt, with only the tiny figures working in the pans to give a sense of its scale. We explored the ancient circular Inca terraces of Moray, where a much younger Leo once camped overnight with friends and a shaman who prepared psychoactive flora to conjure up visions of giants strolling across the landscape.

Peru might be the only place in the world where man’s intervention has made the landscape even more profoundly beautiful. The stepped ridges cut into the mountainsides by the Incas and pre-Incas make the landscape painterly and magical. While you can no longer camp out at the sites, you can eat at Mil, Virgilio Martínez’s new restaurant and food research facility, overlooking the sculpted basins of Moray. I went after one of my day tours with Leo.

You won’t have heard of half the ingredients at a Martínez restaurant, and with everything here being high-altitude in origin, you’re unlikely to eat anything like it again. The rooms – set around a courtyard – are chic and monastic, while the food is a wild mix of tubers, flowers, corns and proteins. It’s intellectual and arresting rather than delicious, but still an ultra-modern cooking.