A staff member films each passenger as we board the deluxe bus from Arequipa to Puno, and again once we’re in our seats. “Por seguridad,” he grunts, without saying what we need to be safe and secure from.

Next, an announcement informs us that if the driver exceeds 90km/h, an alarm will warn him to slow down. The problem, we soon discover, is that our man overtakes on blind corners at that speed. Perhaps the video clips will be shown on the evening news to identify the victims of yet another Peruvian clifftop bus tragedy.

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I don’t really want to leave Arequipa. The Spanish colonial city, surrounded by three photogenic volcanoes, is an architectural gem. Peru’s largest cathedral dominates picturesque Plaza de Armas, a lively public space that everyone gravitates to sooner or later. Santa Catalina Monastery provides a slice of serenity in the heart of the old quarter while San Camilo market offers a raucous contrast. You could eat in a different restaurant every day for a year – although that would mean an awful lot of quinoa.

The bus races into the altiplano, a high, dry plateau of salt flats, stringy grass and inquisitive alpacas.

Puno is 3,830 metres above sea level, yet schoolkids sprint past me on their way home. I can barely walk, have a splitting headache and feel dizzier than after a long night in Lan Kwai Fong. The hotel receptionist makes me a cup of coca leaf tea to ease the symptoms of altitude sickness but then assigns me a room on the 7th floor and apologises because there’s no lift.

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Puno hugs the shores of Lake Titicaca but there are better places to experience South America’s largest and highest lake. It’s a hop and a skip into Bolivia, where the drowsy town of Copacabana serves as a jumping off point for Isla del Sol.

In this low-key traveller’s alternative to the more commercialised Puno, rustic homestays nestle amid terraces cultivated with potatoes, beans and quinoa and the sky is that deep, dark shade of blue you only usually see from an aeroplane window.

Bolivia is the continent’s poorest country and La Paz is a poster child for income inequality. Gleaming office blocks soar above soot-encrusted slums and the streets are gridlocked with minibuses. Dangling power cables fizz aggressively and my guidebook warns of a rise in “violent attacks, including strangling victims and assault with weapons”.

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I head out one morning and find La Paz under lockdown. A huge and very Latin American protest is taking place. “What do they want?” I ask at the tourist information office. “Freedom for their colleagues,” the woman explains. When do they want it? I’m tempted to continue. Immediately, by the looks of things.

Three days earlier, a group of coca farmers were arrested after clashes with the police developed into a full-scale riot. Today’s more muted gathering is to demand their release from custody. So we have a protest to free some protesters and, if it’s successful, they’ll probably organise another protest to celebrate.

Semana Santa, or Holy Week, festivities provide some light relief. A procession snakes past Mercado de las Brujas, or Witches’ Market (potions, lucky charms, black magic), led by a brass band in baggy blue suits belting out infectious riffs while women sporting brown bowler hats twirl and sway to the rhythms. In the 1920s, a shipment of the hard, rounded headgear was sent to British railway workers based in Bolivia but when it turned out they were the wrong size, quick-thinking Aymara and Quechua women snapped up the distinctive hats at a discount. Their descendants still wear the bowler as a sign of pride and cultural identity.

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A scenic trans-Andes bus ride brings me back to Peru, and the world heritage-designated city of Cusco. Tourists thronging the cobbled streets have a dress code, too – many are kitted out in brightly coloured ponchos, alpaca scarves and indigenous-style shawls – Inca chic, let’s call it. Still, if you have an appointment at one of the planet’s foremost archaeological wonders, there’s no harm in dressing the part.

No one tells you before you go to Machu Picchu that the site is located in a subtropical rainforest. Admission and train tickets are only valid on a specified day and if that day happens to be wet or excessively misty, then the highlight of your holiday of a lifetime could end up a washout.

As we chug along the valley floor aboard (mile for mile) the most expensive train ride in the world, passengers scan the skies willing the blue patches to chase away the grey. Thankfully, the clouds clear just in time. Sunshine illuminates the dry stone walls and licks the lawns a vivid green. At the Temple of the Sun, overexcited people in ponchos bellow into their phones. “I MADE IT … YES ... MACHU PICCHU ... TURN ON VIDEO CALL SO THAT EVERYONE IN THE OFFICE CAN SEE ME.”

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The ancient city gets busy by early afternoon but it’s still possible to find quiet corners, away from the crowds, in which to contemplate the genius of the Incas. At about 4pm, the legendary citadel regains its sense of stillness and, by sunset, about 20 of us have Machu Picchu all to ourselves.

Heavy rain is forecast for the following morning and on cue the heavens open. As we board the train back from Aguas Calientes, the nearby town in which nearly all visitors to Machu Picchu spend just one night, I can’t help noticing the disappointed faces of new arrivals. Those are the margins: sunny one day; a complete write-off the next.

Another plaza, another protest. Cusco’s main square this time. Drummers thump, marchers chant and armed police with twitchy trigger fingers glare at demonstra­tors and tourists alike. Then, just when things can’t get any worse, someone starts playing the pan pipes. To escape, I board a minibus to Pisac, a nearby village that boasts a mini Machu Picchu buried in the Sacred Valley of the Incas.

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At the Pisac Tourist Market (never expect bargains at a market prefaced by the word “tourist”), a stallholder adopts that annoying habit of pointing randomly at items and naming them in English for me. “Poncho,” he barks. “Blanket.” “Hat.” “Scarf.” I flinch when he gets to “pan pipes” and head over to the plaza, where a tour group are busy taking selfies.

“Come and have a photo with this lima,” I overhear an American woman say to her partner.

“I’ve told you honey,” comes the weary reply, “Lima is the capital; that’s a llama.”

Getting there

The fastest route from Hong Kong to Peru is to fly Cathay Pacific to Los Angeles and then take Latam Airlines to Lima.