The noise is getting closer. “What if something eats us?” Jane squeaks.

“It’ll probably eat Jane first,” Clare says. “She’s the smallest.”

“Clare!”

“I’m just being forensic,” Clare says. “Animals go for the weakest.”

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“I’m not weak!”

“Anyway, you shouldn’t worry because you’re more likely to be stung by a scorpion lurking in your shoe, which, OK, is horrible, but better than being eaten.”

Being eaten is only one consideration when travelling to Africa with squabbling daughters aged 9 and 7. Civil unrest, filth or being stranded in the desert with a feverish child are higher up my maternal worry list.

But Namibia, with its stable Government and population of only two million, is arguably the cleanest, safest and most efficient African country — and that is why we are here. Public places are pristine. There are good doctors, good drinking water and mobile phone reception almost everywhere.

We are on a fortnight’s camping safari, and tonight we’re sleeping in the immense Etosha National Park; or, rather, we’re trying to. Two lions intent on a midnight bust-up have scattered the jackals and woken us.

We get up to spy on them beyond the campsite’s electric fence, but it is the sound and not the sight of them that terrifies. Those bassy volcanic moans are a visceral reminder of natural law.

Natural law means something in this vast, spectacular country. In a fabulously spacious lorry we travel across boundless deserts, taking in beaches, mountains, palm-fringed oases and sand dunes.

We shower under stars and sleep under canvas, often with only animals for company, while temperatures range from sub-zero to 40C. It’s winter in July, and we need warm gloves, sunscreen and adaptability. The children are more adaptable than me. I think of lurking mambas and puff adders.

“You’ll never see a snake,” Gabriel and Kaleb, our guides, say with a laugh, and while it’s true that we never do this doesn’t stop me mincing like a pantomime dame through the bush for the entire fortnight. Yet we’re safe as houses out here where there are none: Gabriel and Kaleb can get tyres out of deep sand, administer first aid and cook fantastic suppers in campsites so remote that the flushing loos and swimming pools are always a surprise.

So is the pool water, which emanates from deep boreholes and is astonishingly cold. While the children dip their toes, shrieking hysterically, I muster a hearty crawl. Once, local onlookers express concern. “Don’t worry,” I chirp, “I’m English,” before emerging tremulous and dizzy. I have hypothermia, in the African midday sun.

There are ten of us, including the guides, from four countries, and though we speak English together, the girls learn to count in Italian, say “Your feet smell” in Flemish and “I love toasted marshmallows” in Damara. This is why I brought them, I think, as they thrill to the novelty of it all.

Since my husband proposed to me on holiday in Zimbabwe I’ve dreamt of returning to Africa. It means leaving our youngest daughter, Celia, behind with him, which breaks my heart, but it’s worth it to see our older daughters chewing on a kudu kebab or clambering over rocks to find hidden Bushman paintings. The girls are in heaven.

As far as Jane is concerned, we’re in Namibia for its thousands of elephants: both girls fairly weep with joy at their downy-fringed infants. On each game drive the first sighting of any creature produces whoops of excitement from children and adults alike.

Clare, who likes order, classifies everything we see with the uncanny precision of a naturalist on board a 19th-century exploratory ship. Sightings are grouped in her notebook into Uncommon, Common, Very Common and Rare. Jane remains glued to the truck windows. She is the first to see a meerkat and the only person to spot an aardvark. Speak to her, she doesn’t hear: fascination has rendered her catatonic.

It seems miraculous that Namibia, with an annual rainfall of less than 9cm, sustains any life. Even in Damaraland’s gorgeous mountains there is little greenery; and the open savannah of the Namib desert, with its flaxencoloured grass, is suggestive of American prairie crops — until you remember that there is no water.

Survival out here has required legislation. Tourism is largely responsible for strict conservation laws, and in the enclosed village of Kamanjab the ancient Himba tribespeople sell jewellery and charge fees for visiting them in their clay huts where, instead of washing, they cover themselves with red ochre paste. We get a near-Stone Age experience; they can buy diesel for their water pump.

Clare and Jane, both blonde, fascinate the Himba children: their hair is pulled and a young girl steals their hair-ties. Then a toddler catches a stray plastic bag and punches holes in it, improvising a sleeveless top.

Soon, though, our attention is distracted when two men return from hunting a giraffe. It’s already in pieces, being too heavy to move whole: the ribcage is armchair-sized and they hack at it with machetes. Limbs are balanced in trees so that the meat can dry — not everybody’s idea of a holiday view. “Can we go now, Mummy?” the girls plead.

After that the luxury of Swakopmund, Namibia’s premier coastal town, seems surreal, though we enjoy its Olympic-sized pool and Tug restaurant, which protrudes jetty-like into the Atlantic, and shopping for presents in the friendly wood market.

We see a real leopard at the Okonjima Africat Foundation, a magnificent 65kg male up a twisted tree chewing a carcass. Exquisite, disdainful and lethal, it can tackle prey twice its weight. That’s a rugby prop forward, at least. “That’s alarming,” Clare says.

We accelerate away in a cloud of dust, until we encounter several cheetah. Circling the vehicle lazily, they seem scrawny compared with the leopard but their strong, swanky hips can propel them at 75mph towards lunch. Jane says: “I’m glad I live in England.”

Into the Namib desert, and the challenge is not cats but heat. We feel impaled by it. After a stop at the bakery in Solitaire, we camp within reach of Sossusvlei and its colossal sand dunes. Our aim is to climb the highest at sunrise, then hike across a dune field so illusory that we could be dreaming — or in a Dalí painting.

It’s a rolling orange moonscape, studded with 2,500-year-old shrubs, no place for human beings. But it is Clare’s overall favourite. As the rest of our group returns to Windhoek, the girls and I turn east to the Kalahari on a two-day visit to the Bushman tribe In the township of Gobabis, which we visit en route to the Bushmen, families live in houses made from plastic sheeting, sacks, sticks and cardboard. No one has running water or loos.

My daughters fall silent. In some ways the Bushmen seem barely better off. Hunting is now banned except with permits in strictly designated areas, which is good for wildlife but not for a tribe of hunter-gatherers, most of whom rent space on farms. But they are all smiles when we arrive: a fire is lit, and over tea and hot roast vegetables in the dark we talk, with our guide, Peter-Hain, and one Bushman translating. I ask what happens when people grow old, but wish that I hadn’t. If the tribe needs to move, the infirm are left behind with some food. When it’s finished, so are they.

At dawn the following day we are greeted by 15 men, women and children in loincloths. Hunting techniques are demonstrated and when the men creep silently through the bush, skinny legs taut, bows and arrows outstretched, I realise that they look exactly like the rock paintings of their forefathers.

The women, meanwhile, are busy making jewellery: ostrich eggs are painstakingly chipped into minuscule beads, while Clare, Jane and the Bushman children exchange English tag for African spiral dances.

Later that night, our last, I consider how the happy sight of the children playing underlines the simplicity of Peter-Hain’s vision. When finally we depart, after a singing and dancing display of ethereal beauty, the men quivering, the women and children swaying, our world feels strangely, wonderfully amplified.

Mary Loudon’s latest novel, Relative Stranger: A Sister’s Life After Death, is published by Canongate at £6.99

Need to know

Wilddog Safaris and Crazy Kudo Safaris (00 264 6125 7642, wilddog-safaris.com) has a 13-day family adventure from £1,220 per adult, £1,075 per child. Shorter safaris are also available.

Three-day Bushman tours with Uakii Wilderness (00 264 6256 4743, www.uakii.com) cost about £300.

Getting there There are no direct flights between the UK and Namibia. BA (ba.com), South African Airways (www.flysaa.com) and Virgin Atlantic (virgin-atlantic.com) have flights to Johannesburg, with connections to Windhoek. The cheapest return flights are £844.

More information No visas are currently required for UK citizens for leisure trips to Namibia.

Vaccinations and antimalarials are recommended. Ask your GP.

Chris McIntyre’s guidebook Namibia (Bradt, £15.99) proved invaluable.

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