Jade from Adelaide is giving me the VIP treatment ("because this is what it means to travel in Gold Kangaroo class"). "If you need me, I'll be in there," she says, pointing to what looks like a cupboard along the corridor. "Just press the button." I'm glad my space looks more comfy than hers, as I'm about to begin one of the great train marathons of the world, taking me more than 1,800 miles from the sweltering tropics of Darwin through the blistering red desert of Alice Springs to Jade's home town, where the waves roll in from Antarctica.

The drama started well before the two mighty General Electric locos backed down on to their carriages at the frontier town of Katherine. The day before, Cyclone George, swirling in from Singapore and points east, had slammed into Australia's Top End and blown away 15 miles of the railway south of Darwin. Not exactly what I had in mind, since I had come 8,500 miles from the UK to travel on The Ghan's "indestructible" tracks. The world's most modern long-distance railway, The Ghan's route was completed in 2004, when the Adelaide to Alice Springs line was extended north through the desert to Darwin. Despite the cost of AS$1.2bn (£500m), I began to wonder if we'd advanced much from the pioneering days of the 1920s, when termites ate the wooden sleepers and trains would often be halted for two weeks at a time – with the driver having to shoot goats in order to feed the passengers.

At the best of times, Darwin railway station is no St Pancras or Grand Central. It is stuck, surrounded by rusting stacks of containers, on a bleak peninsula, miles from town. But today it is not even dignified by a train. " OK folks, we're going by road," proclaims Curtis, the chief steward, his conductor's uniform in surreal contrast to the convoy of school buses lined up on the platform. "Even that's washed away, and the driver may turn back. In which case, we're going by plane."

Curtis passes down the bus handing out "sanders" and " stubbies " from a coolbox. "Just my luck," he says. He was also in charge when the train came off the tracks last year after running into a drunken truck driver on a crossing. Inevitably, intrepid outback driving and Aussie humour win through. "Shame they didn't put floaties on the loco," someone quips. And after a jolting and sweaty four hours of slithering across red mud, shattered tarmac and torn-up trees, there before us is the train – a shimmering mirage, its air-conditioning humming like a fridge.

But my adventure isn't over yet. I sneak up to snap the locos and the driver leans out, yelling "Get back!" Australia, like Britain, currently has problems with train spotters because of terror fears. So I wave my ticket at him. "Look behind you!" he shouts. And slithering behind me is a 5ft black snake. (I discover afterwards it is a highly poisonous relative of the cobra, though understandably, I don't stop for an inspection.)

Snuggled in the safety of my berth, I am happy for a while to observe the outback less intimately, as we begin to roll south towards Alice Springs. We're a relatively light load today – a mere 24 coaches – but the "legendary Ghan", as the Great Southern Railway likes to call it, has run in the past with "47 on", a length of nearly a mile. We head on into the afternoon, slowly always, and sometimes pulling over for the vast freight trains that are the reason for the line's existence. " The freight pays, the passenger stays" is the unofficial slogan.

As the southern sun hots up, swamp and eucalyptus give way to saltbush and spinifex. But no sign of the camels which helped to give the train its name. Allegedly, The Ghan was named after the Afghan drovers whose camel trains were made redundant when the first section of the line was opened in 1929. The drovers went home and set their camels to run free. Believe it if you like. But it is a fact that there are more camels in Australia than in the entire Arabian peninsula.

The present-day Ghan is something of a curiosity among the great trains of the world – neither a luxurious hotel on wheels like the Orient Express, nor a workaday means of transport for "real" passengers. The vaguely Art Deco coaches are not particularly historic – unless you are a railway enthusiast who spots 30-year-old vehicles from the US stainless steel era. There is another odd quirk: The Ghan is operated by a subsidiary of the British company Serco, which also supplies electronic tags to the Home Office and operates some of Britain's speed cameras. (No wonder The Ghan runs so slowly.) Yet for a very grand train, it has a unique lack of swank, as backpackers heading for the "red centre" mix with plane phobics and the "holiday-of a lifetime" set.

And then there is the scenery. Some say The Ghan is boring, unless you like large helpings of desert and the colour red. But tonight, with the smell of dinner being cooked in the kitchen car and the sun mellowing from the iron heat of the day into a huge, soft red disc over the outback, there is a profound sense you are somewhere special. On the menu is pumpkin and bush honey yoghurt soup, followed by Northern Territory salt water barramundi which, with a couple of glasses of South Australian riesling, is the perfect prelude to the womb-like sleep that is one of the pleasures of night train travel.

Walking back to my berth, there is a hint of the scent of the outback – the purest air in the world – through the gaps in the swaying corridor connections. And the stars through the window might possibly be the brightest you will ever see outside space. Here you could slumber in the perfect solitude, except you know that in the blackness of the desert outside the windows are the wombats, the roos and the bilbies – the animals of the Australian night.

At Alice Springs, where we pull in next morning for a four-hour stop, there is a proper chance to get the desert between my toes. It's 36C in the shade, and has rained only three times in the past two years. Someone tells me: " You're welcome to drink the water from the springs, but spit the sand out first." I avoid the opportunity to lunch locally on fillet of camel or buffalo steak with witchetty grub dressing. Instead I take the bus to the Alice Springs Desert Park, where the wildlife survives uncooked, and learn all sorts of useful things about the outback. (For example, did you know that the sand isn't really any more red than at Bondi or Blackpool? The redness is apparently caused by a fungus.)

Back on the train, another day and another night. The scene outside the window unfolds like a Planet Earth webcam. We are now morphing into our third climate zone – the soggy greens of Darwin and the hot ochres of Alice are being replaced by the deep yellows and golds of the grain-growing south. The sight of the first tree seems almost as strange as the desert once did. Supper is grilled kangaroo loin – and once more the dreamiest sleep. Until, that is, a jolt in the small hours means the diesels have uncoupled for refuelling. We are at Tarcoola, the junction with Australia's other great transcontinental route, the Indian Pacific, which still makes its leisurely way from Sydney to Perth.

Arrival at Adelaide is a mere 20 minutes late – not bad after a journey of 48 hours. Curtis has filed his log and is chuckling about the passenger who expected the morning's newspaper delivered to his berth in the middle of the desert. Luckily Jade didn't get too many buzzes during the night and is planning to pop home to Mum. I shake hands with Tom, the head chef, who is off to source some more goodies in Adelaide's Central Market. With two trains in each direction a week, there's a lot of cooking to do. As for me, I'm heading for one of the lush little wineries in the cool of the Adelaide hills, where I'll toast the fact that it is still possible to get up close to the remotest and most mysterious places on the planet from the comfort of a seat on a train.

Getting there

There are no direct flights between the UK and Darwin or Adelaide. Connecting flights to Adelaide are available with Cathay Pacific (020-8834 8888; www.cathaypacific.com) via Hong Kong, and Malaysia Airlines (0870 607 9090; www.malaysiaairlines.com) via Kuala Lumpur; or to Darwin with Royal Brunei Airlines (020-7584 6660; www.bruneiair.com/uk) via Bandar Seri Begawan. "Open jaw" tickets, flying into Adelaide and out of Darwin (or vice versa) are available with Qantas (0845 774 7767; www.qantas.co.ukuk), with the subsidiary Jetstar Asia making up the Darwin-Singapore route.

To reduce the impact on the environment, you can buy an "offset" from Equiclimate (0845 456 0170; www.ebico.co.uk) or Pure (020-7382 7815; www.puretrust.org.uk).

Bespoke itineraries in Australia are available with Tailor-Made Travel (0845 456 8050; www.tailor-made.co.uk). An eight-night itinerary, including two nights' accommodation each in Darwin and Alice Springs, a three-night tour of Arnhem Land and a one-night trip on The Ghan from Darwin to Alice Springs starts at £1,185 per person. International flights are not included but can be organised at an additional cost.

Getting around

The Ghan (00 61 8 8213 4444; www.gsr.com.au ) travels between Adelaide, Alice Springs and Darwin with a journey time of two nights in either direction. A Gold Kangaroo sleeper ticket between Darwin-Adelaide costs A$1,920 (£800), full board.

More information

Tourism Australia: 0870 556 1434; www.australia.com