Extreme safari: Rhino, wildebeest, whistling frogs – there's a new species to discover around every corner at the Phinda game reserve

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The adrenalin coursing through my body takes me back to the feeling I had jumping out of a plane – only this time I'm not at 14,000ft but firmly on terra firma, sat in the back of a car. The hairs on the back of my neck are on end, my pupils dilated and my heart thumping over the rustle of the breeze.

I am in Phinda, a game reserve owned by the &Beyond luxury-adventure company, in the South African province of KwaZulu-Natal, on the eastern coast of the country and, as our 4x4 has turned down a small tree-lined track, we have come face to face with three white rhino: a bull, a female and their calf. Though ordinarily placid, today, we are told, the rhino's acute hearing has been interfered with by the wind and they seem on edge. The bull is particularly unhappy with our presence and takes some threatening steps towards the vehicle. Intimidated by our proximity, he lurches forward suddenly, but luckily within a couple of feet he is startled by the clapping and shouting of our rangers, Daryl and Bernard, and backs away. I'm shaken – but what a moment.

It is easy to fall into the list-ticking game on safari, but the first lesson I have learnt is that it is nature – not any inventory – that dictates what the next scene will be. Growing up in rural Wiltshire, I have always felt alive surrounded by the smells, sounds and sights of the outdoors, but nothing has been close to the 56,800 acres of wilderness at Phinda, home to 421 different species of birds and 74 species of mammals, including the rare black rhino. In fact, Phinda has a growing population of these threatened creatures and offers a specialist safari allowing visitors to track them on foot.

Known as "The Seven Worlds of Wonder" for its seven distinct habitats – comprising palm veldt, savanna, wetland, sand forest, broadleaf woodland, riverine forest and Lebombo mountains – Phinda offers an extraordinarily compact experience of South Africa's landscapes. Guiding us through the wilderness is specialist ranger Daryl Dell, who has worked here for seven years. His endless dedication to the reserve and its abundant wildlife and plants is inspiring. Indeed, despite being surrounded by such large and spectacular beasts, one of his main interests lies in the more modestly sized frog – at every opportunity, he talks enthusiastically about "frogging" and his ongoing search to discover the rare "whistling tree frog" on the reserve.

Around every corner is a new attack on the senses. From the delightfully named and sweet-scented "forest num-num" that grows among the woodland and grasses, to a cacophony of frog calls after the rain in the marshes and the sight of wildebeest emerging out of heavy mist, eerily reminiscent of a scene from The Hound of the Baskervilles. As dusk falls on our return home to the luxurious Mountain Lodge, we happen upon a live necking show. Not a couple of honeymooners, but an innocent display of 13 young giraffes playfully landing firm blows on each other – a truly extraordinary scene.

The highlight of my trip, however, is catching a glimpse of an elusive cheetah and her cubs. From an initial introduction of six cheetah to the reserve in 1991, their numbers have remained stable at between 20 and 30 in the past five years, making Phinda one of the best places to see and photograph them in Africa. Having waited patiently for the mother and her cubs to waken and move in search of their next kill, we are rewarded by the cats crossing within metres of our vehicle. They seem at ease in our presence which, in turn, gives me the time to capture their incredible feline beauty on film.

This summer, South Africa will host the continent's first football World Cup, attracting more than 500,000 visitors. Fans will no doubt be hoping their teams provide them with enough of an adrenalin rush. Should it fail to materialise, they could do worse than get their fix from a visit to the breathtaking land of Phinda.

Full board, safari activities and nature walks at &Beyond Phinda Mountain Lodge from £285 per person, per night (andbeyondafrica.com). Emirates (emirates.com/uk) offers return flights from London to Durban via Dubai from £571.60 per person, including taxes