The route is not serviced by one of China’s superfast bullet trains, which can travel up to 350km/hour, but by a K class train that, according to the screen inside each carriage, averages 92km/hour.

K class trains offer three classes, the cheapest being the aptly named “hard seat”. Although not actually hard, the seats are almost vertical and can’t be adjusted. Carriages can be noisy and crowded with standing passengers.

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Then there’s the “soft sleeper”, the equivalent of first class. The compartment is wider than the hard sleeper and has a door that can be shut.

There are two columns of double bunk beds measuring 75cm x 190cm plus a table by the window. Tickets are advertised at 997.5 yuan – about US$138 – but the best price my travel agent could do was US$200, and that was in the winter.

“In the summer, even if you give me US$1,000, I can’t 100 per cent guarantee a soft sleeper,” said Shang Qin, of Adventure & Tour China in Chengdu. “In the summer, all 128 soft sleepers are sold within seconds of being released. I would have to hire 128 scalpers to guarantee you a ticket.”

Ticket in hand, I arrive at Lhasa Railway Station an hour before the 7pm departure as instructed. My luggage is X-rayed and a pair of scissors is confiscated by security. I am then directed to a waiting room the size of a warehouse, with thousands of people inside.

At 6.30pm, a loudspeaker crackles and says something in Mandarin. A series of doors open and passengers sprint to the platform.

With a large suitcase I can’t move fast. By the time I reach the platform, long queues have formed in front of the doors for the hard-seat carriages. There are no queues for the sleeper carriages.

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I show my ticket to a conductor, who then shows me to my compartment, which is spotlessly clean.

My bed is more comfortable than those in most of the hotels I stayed at in Tibet: soft but firm, with a thick duvet and large pillow. There is an electric socket and USB charging port by my bed, a reading light and a large curtained window to take in the view. The entire train is no-smoking – an anomaly in China.

All three people I share my compartment with go out of their way to make me feel welcome in China. There is an Christian Evangelist who speaks very little English and a young father and his seven-year-old son who speak no English at all.

But that doesn’t prevent us from striking up a rapport using sign language and the translator apps on our phones. We share snacks and a few jokes, and we keep an eye on each other’s luggage whenever one of us wants to stretch their legs or use the bathroom.

Night falls shortly after we depart. I read a novel on my Kindle, Seven Years in Tibet (1953), and fall asleep to the click-clack sound and vibration of the rail tracks.

At 6am I awake, put on my shoes and walk to the bathroom: a room with two hand basins, a hot water dispenser and three toilets with locking doors, two of which are filthy. It appears the toilets are cleaned by conductors during the journey but cleaning does not happen often enough. Toilet paper is not supplied and there are no showers.

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After freshening up at the hand basin, I head to the dining car, which consists of about a dozen small booths. Most are occupied by hard-seat passengers trying to steal a few hours of sleep under harsh fluorescent lights.

At 7am, a conductor kicks them out so the breakfast service can begin.

Breakfast is a set menu plate of rice, pickles, stir-fried vegetables and a steamed pork bun: nothing I can stomach at that time of the morning. There is an à la carte menu but it is in Mandarin and, based on the photos, contains solely stir fries.

Instead I buy a bottle of orange juice for 10 yuan and graze on a bag of sultanas I bought in Lhasa.

At midday I buy a big cup of instant noodles for 8 yuan.

I spend most of the day reading and taking in the high-plateau scenery, which varies from pancake-flat desert to Eurasian steppe to jagged mountains dusted with snow.

We zip past frozen brooks and rivers, abandoned stone and mud-brick villages that could be sets for period kung fu films, and a cobalt-blue lake that is so wide I can’t see the other side.

I also walk from carriage to carriage. The hard seat carriage is not the chicken-fight I imagined. There are no standing passengers and it doesn’t look dirty. Hard seats look fine for travelling during the day but not for overnight, unless you’re on a tight budget.

At 5pm we arrive in the city of Xining, Qinghai province, and change trains.

The transfer is easy: the second train is waiting for us on the other side of the platform and my seat number doesn’t change. But I am sad to learn my new friends are not going any further.

I shake hands with the preacher and the father while the boy, whose name I cannot understand, pronounce or remember, hugs me.

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I share my new compartment with two middle-aged Chinese men who reply when I say “hello” but don’t make small talk. They fall asleep on the top bunks early in the evening and I do not see them again until the following morning, when a conductor walks into our compartment at 6.30am to wake us up.

The journey terminates at Chengdu station bang on schedule, at 7am.

Overall, it was a comfortable and interesting journey that cost about the same as a flight. I saw new parts of China but the views couldn’t compete with those in Tibet.