That evening had been about as good as it gets; we had filed silently behind our armed tracker to a bluff over the river where hundreds of hippos wallowed, grunting, puffing and snorting like old men at the bar over a rather risque joke. They're not really the kind of animal you immediately bond with, but it's almost impossible to believe that hippos are probably the most dangerous species in Africa, and that it is a decidedly bad idea to get between them and the water.
Almost as many crocodiles were snoozing in the mud, and a few puku, the rather refined chestnut-coloured antelope, with ever-so dainty habits, eyed the river nervously and thought better of it. Overhead, flocks of egrets returning home to roost pierced a vermilion sunset, and that tightrope- walker among birds, a lone bateleur eagle, performed his last balancing act of the night, soaring in the thermals.
We were somewhere in the middle of Zambia's South Luangwa National Park, one of the several contenders which include Tanzania's Serengeti or Ngorongoro Crater, and South Africa's Kruger, to top the bill as Africa's best game park.
At 3,493 square miles, South Luangwa may not be the largest park, but few can match its abundance of game and lack of visitors. Limited communications, roads and lodges keep the minibus brigades at bay, and the designer safari set who need gold bath taps in their tents, polished teak floors and cordon bleu cookery haven't got this far yet.
Our tiny bush camp consisted of four thatched huts with earth floors - a tree grew through the middle of one of them - and a lion could have walked straight into the bedroom, though our only unlicensed nocturnal visitors were a pair of honey-badgers which regularly raided the open kitchen, leaving their footprints in the butter. The dining room was a table under a tree; the camp's luxury feature: a hammock.
It was here in South Luangwa Valley that the idea of the walking safari was born, pioneered by the late Norman Carr, who first came to Luangwa Valley as an elephant- control officer in 1939, and ended up as Zambia's Grand Old Man of conservation - 8,000 people including former president Kaunda attended his funeral in April 1997, and his tomb in an ebony grove in the park is now something of a place of pilgrimage for his many disciples. Originally attracting publicity a la George and Joy Adamson in Kenya, by raising two orphaned lion cubs and returning them to the wild, Carr's contribution to Zambia's wildlife went much, much further.
It was he who in the early 1950s persuaded Chief Nsefu to turn some of his land into a game reserve and open it to the public for the benefit of both the wildlife and the local community - a policy which more than 40 years later is only now being recognised as the way forward elsewhere in Africa.
The Carr family still runs Kapani Lodge at the entrance to the park where we had met on arrival before our bush camp adventure. With its ceiling fans, even a pool, Kapani is comfortable by Zambian standards, but by no means the kind of luxury ghetto typical of many safari lodges, and the villagers pop in and out at will. Life in these rural areas is very much at basic subsistence level, and any jobs generated by tourism are much needed.
Before heading into the bush, we'd already taken a couple of game drives, one of them at night (not allowed in many countries) to bone up on our genets, our civets, jackals and porcupines that instantly freeze in the spotlight and then melt away into the blackness. It was an eerie, spine- chilling scream that alerted us to our first sighting of a Pels fishing- owl, its cry described by an ornithologist "like a man who has lost his soul falling down a bottomless pit".
In contrast, the elephant who had just lost her baby to a huge crocodile remained mute, ceaselessly pacing the river-bank; Abraham told us she would probably circle the area for days afterwards.
Trained by Norman Carr whom he met as a boy, Abraham now trains and examines other local guides and helps the valley's Schools Project to pass on the conservation message. Since the 1950s, the elephant population has been reduced by poaching to 15,000, and despite the efforts of Norman Carr's Save the Rhino Trust, the black rhino has been wiped out completely - its horn, in its powdered form, is considered a powerful aphrodisiac in the Far East.
It was Abraham who was to accompany us to the bush camp for our walks in the wilderness in search of our rainbow. So we rise before dawn and stride, wannabe Hemingways with our compasses, provisions and armed guard. But Abraham is not a gung-ho leader, and safari-virgins anxious only to notch up the Big Five and get back to their sundowners might feel frustrated. "Some holidaymakers have seen too many wildlife documentaries," he explains. "They expect a chase, a wham-bang kill, and they want it all on their videos. They forget that the TV versions may have taken up to three years to film." In fact, you'd be incredibly unfortunate not to spot a great variety of animals, and many of the 350 species of birds in the Luangwa Valley. Its range of habitats, from open savannah, riverine woodlands and ox-bow lagoons are a Garden of Eden for huge herds of elephant and buffalo, lion, antelope, giraffe, even the elusive leopard.
Under Abraham's guidance, we gradually begin to fit the pieces of the wildlife jigsaw together, and understand just a little bit more of the rhythm and pulse of life in the bush. An apparently empty dried-up river- bed becomes an instant map and visitors' book. Those chalky droppings belong to a hyena which probably has the world's most efficient digestive system; it can crunch and absorb every morsel of bone, hair and offal. The scattering of apple-ring pods from the winter thorn are clues enough that an elephant has passed through, not long ago according to dung which Abraham crumbles. Elongated toeprints indicate leopard, though he'll be holed up during the heat of the day; stubbier tracks reveal the presence of lions, but if they get restless we'll get plenty of warning - from the hysterical chatter of the vervet monkeys in the trees, the bark of the baboons or the strange whistling from a puku herd.
Of far greater concern are the solitary prints of a buffalo, a Kakuli, the local name for an old buffalo that has left the herd probably to die and one of the most dangerous species on the plains. We hope that the human footprints we come across are not those of a poacher. "More likely a lad in search of the local Viagra, the bark of the balanite bush," reckons Abraham.
But lion, elephant, buffalo and leopard fade into dusty perspective as, late in the afternoon, we come upon one of the most wonderful sights in Africa. The trees along the river-bank, gaunt and skeletal elsewhere, seem to have burst into flower with exotic candy-striped blossoms. And then, as we approach, there's a sudden brilliant explosion of carmine pink, metallic blue and emerald green.
We have found a colony of the world's most beautiful bird, the carmine bee-eater. Every autumn thousands of them return to nest in the same spot in the Luangwa Valley, where the river-banks are pitted with thousands of burrows. Like priceless flying jewels, they swoop, dart, wheel around us... we have walked into the promised rainbow.
Jill Crawshaw travelled with Wildlife Worldwide (tel: 0181-667 9158). An eight-day tailor-made holiday in the Luangwa Valley starts from pounds 1,675 per person, including flights, full-board accommodation in lodges and bush camps, and guided safari drives and walks. (The best time of year to catch the carmine bee-eaters is from mid-September until May.)
Other operators include Okavango Tours and Safaris (tel: 0181-343 3283) which offers an all-inclusive18-night safari in three of Zambia's national parks, from pounds 4,664 per person, and Sunvil Discovery Africa (tel: 0181- 232 9777), which arranges one-week all-inclusive safaris in Zambia from pounds 1,550 per person.
Contact the Zambia National Tourist Board, 2 Palace Gate, London W8 5NG (tel: 0171-589 6343; fax: 0171-225 3221).
The Bradt Guide to Zambia by Chris McIntyre (pounds 11.95) contains some excellent background information.