But the locals are still waiting for the tourists ...

The flood came before dawn," recalls Sevenoy Letoiye, the manager of Elephant Watch Camp in one of Kenya's leading game parks. Early on the morning of 5 March, a wall of muddy water surged down the valley from the Kenyan highlands, sweeping across the Samburu National Reserve and engulfing everything in its path.

"The noise of the water woke us all," Letoiye says. "We managed to drive our guests to a safe place with higher ground."

Having rescued their guests, the staff of Elephant Watch waded back in the dawn light to try salvaging what they could from the camp. "I climbed on a roof, then I saw it was getting even worse and I climbed a tree," Letoiye says. "I stayed up there for five hours. It was scary." He watched as the torrent took down four trees, including one that had a troop of baboons in it.

Today, the coffee-coloured Ewaso Nyiro River – the provider of life to this otherwise arid part of Africa – flows placidly past the campfire area, where a hammock swings from a giant fig tree. Letoiye was born after the river last flooded to the same extent, in 1961, long before safari camps had brought job opportunities and extra income to this part of northern Kenya.

We're standing in the camp's magnificent "mess tent" – a kind of bush living room with a high, sweeping roof – deep in the riverine forest of the reserve. Birds call in the drowsy afternoon heat.

Just downstream is the research camp of Save the Elephants, the foundation run by the conservationists Iain and Oria Douglas-Hamilton, who own Elephant Watch Camp. Of the 11 safari camps in the reserve, the nine built along the river were destroyed. Everything that wasn't firmly planted in the ground was washed away; what was left – foundations, walls, wooden pillars – was smothered in three metres of thick ooze and debris.

Five people living further downstream were swept to their deaths. The cause is unknown but rumours are that ruptured dams on farms to the south were to blame.

Elephant Watch, in common with all but two of the riverside safari camps, reopened within months. The camp is delightfully constructed of materials from the bush (dead wood, clay and thatch) with a little canvas, and swathes of funky, multi-coloured fabric. The deliberately light environmental footprint makes repairs relatively easy.

Although some smaller animals were swept away, most of the area's wildlife survived, having instinctively moved uphill from the river. None of the reserve's elephants or arid country specialities – the rare grevy's zebras, beisa oryx, reticulated giraffes and long-necked gerenuk antelopes – was lost.

But tourist bookings have slumped in the wake of the flood. I was told that there were fewer than 100 other visitors in the reserve, though it has some 500 beds. It's a far cry from the thousands who crowd the key game-viewing areas of the Maasai Mara, Tsavo and Amboseli parks in southern Kenya.

For the local community, getting safari tourists to come back to Samburu, paying the £40-per-day entrance fees, is a priority. The British Army, which has a training base in northern Kenya and helped with the flood rescue, is rebuilding a key bridge linking the two halves of the reserve, due to be finished by the end of the year. When it reopens, visitors will again be able to explore the freshwater springs and plains on the south side of the river and the forest-fringed meanders on the north bank on the same game drive.

It is game drives – excursions in open-top safari vans – that brought me to Samburu. I'm woken at 6am by a raucous dawn chorus – babbler birds, I'm told, screeching outside my tent. Primed with strong Kenyan tea, I'm soon on the hunt, standing in the back of the vehicle, holding tight as we bounce along the track with the sun striking horizontally across the savannah. To the north, gaunt hills and mountains rise. Closer to hand, the river's course is traced by the fantastical branching shapes of doum palms, with their weirdly forked trunks. We all have grins on our faces: the physical experience alone is fun, leaving aside what you might see.

But word is out on the bush telegraph that a leopard has been spotted near the camp and I gaze eagerly into the branches of every flat-topped acacia tree. First stop is for a secretary bird, a tall, prehistoric-looking snake- and-insect catcher. It minces menacingly through the tall grass, flicking the quills on its head and examining the ground lopsidedly for just the right morsel. It grants us a three-minute appointment, then turns its back and disappears.

As we drive across a dry stream bed we encounter a young crocodile, one metre long, possibly surprised by inexperience at the arrival of daylight (they're habitual nocturnal wanderers). The crocodile sinks to the ground and plays dead, although one glittering eye watches our every lens change.

Next, we're surrounded by a harem of impalas – the sexiest antelope on the plain, with their doe eyes, glossy rumps and neat, white ankle socks. The lyre-horned buck stands sentinel as we admire his wives. We drive off and are still watching the impala recede when we have a gerenuk demonstration on our left. This "giraffe antelope" stands vertically on its hind legs to crop the best leaves, like someone changing a light bulb. Then, in a seamless segue, a group of spectacular, parallel-horned beisa oryx – supposedly the inspiration for the unicorn myth – is on our right.

The animals are coming thick and fast. A little further on I see the russet patchwork of a giraffe's neck. It's the rare reticulated giraffe. Our eyes attune and we're watching a whole herd, their purple tongues curling around the choicest browsing, their silent, slow dance through the trees a rhythmic image that seems familiar despite the new intensity of seeing it in the flesh.

I'm still looking out for the leopard, but as we emerge from the trees near the river, all feline thoughts are forgotten as an unmistakable, huge, grey shape moves into view ahead of us: an elephant. We stand breathless and transfixed for half an hour as members of a herd go about their morning business – emptying their bladders in a loud gush, inspecting each other's dung with sensitive trunks and knocking over small trees for a mouthful of tender thorns and leaves. Glimpsed fleetingly between the legs of the matriarchs is a baby so tiny that our guide thinks she must be only a fortnight old.

Her back is covered in soft brown hair; her trunk seems too short and she probes with it at everything. Her ears are too big, I think, but she'll grow into them. Two teenaged male elephants cross the track a little closer to our vehicle than the others. The nearest one pauses, just 10 metres in front of us, swivels in the dust and affects a cocky, legs-apart pose, ears flapping, trunk swinging. His friend does the same, a little too late to be convincing.

With the heat building, the morning game drive's three-hour span is over, and we all have a date with a big breakfast. Grevy's zebras in perfect reverse-pin-striped attire flick their tails and lift their heads as we pass, blithely unaware of their endangered status. Fewer than 2,500 of these zebras survive, many of them in this unfenced sanctuary of 300 sq km (the size of the island of Jersey), where they come and go at will and their human neighbours have agreed to stay outside with their goats and camels.

Back at camp, I soon hear that other guests have seen the leopard. I'm not miffed. They didn't see our dazed croc-out-of-water, our punctilious secretary bird. And they didn't share our encounter with that infant elephant.

The leopard will still be playing hide-and-seek when we go out again later: what a perfect way to spend a day.

Richard Trillo is the author of the 'Rough Guide to Kenya' (£16.99), and runs the Kenya travel blog theroughguidetokenya.blogspot.com.

Travel essentials: Samburu

Getting there

* The writer travelled to Samburu as a guest of Kuoni (01306 747008; kuoni.co.uk) and the Kenya Tourist Board (020-7367 0931; magicalkenya.com).

* Kuoni offers a 10-night Kenya itinerary from £2,340 per person. It includes flights from Heathrow on Kenya Airways, domestic flights, game drives and ground arrangements with Private Safaris. Accommodation comprises two nights at The Norfolk in Nairobi (with breakfast), one night at Treetops in Aberdare National Park, three nights with full board at Samburu Intrepids and four nights all-inclusive at Dream of Africa in Malindi.

* British Airways (0844 493 0787; ba.com), Kenya Airways (020 8283 1818; kenya-airways.com) and Virgin Atlantic (08705 747 747; virgin-atlantic.com) fly non-stop from Heathrow to Nairobi.

Staying there

* Bookings for Elephant Watch Camp are taken through the Nairobi office (00 254 20 889 1112; elephantwatchsafaris.com). An overnight stay for two people costs from US$1,100 (£733), full board with activities.

Red tape

* British passport-holders require a visa to enter Kenya. You can buy one on arrival at Nairobi airport, with minimal bureaucracy for US$25 (£16). The fee is being raised to $50 (£33) from 1 January next year (020-7636 2371; kenyahighcommission.net).