I’ve never quoted Winston Churchill before, but when he described Uganda as ‘the pearl of Africa’, he was right. Imagine a place that has the continent’s tallest mountain range, some of its best wildlife, the source of the Nile and a near-perfect climate, all in a country the size of the UK. This is pocket-sized Africa: intimate, unspoilt and one of the best antidotes to London living I’ve ever had. What’s more, it’s not yet on the package tour trail.

Uganda has emerged from Idi Amin’s shadow as a shiny new destination for exploration. I was there for a week in November and was quickly seduced. It started while I was looking out of the window of our overland truck driving west from the capital, Kampala. The sprawling suburbs slowly coloured a bright, almost luminous green as houses were replaced by rolling hills that looked like reams of soft fabric. With our guide’s help, I was able to distinguish between wheat, millet, papyrus, maize, bean and potato crops, and to spot the tall poles of sugar cane and the shorter umbrella shades of cassava. Eighty-seven per cent of Ugandans live rurally, cultivating these crops for home along with coffee, tea and fish for export.

Wildlife is the big draw, and although Uganda’s parks have neither the scale nor the abundance of those in Tanzania or Kenya, they nonetheless contain plenty that’s thrilling and, thankfully, don’t heave with tourists. The real treasures are in the country’s southwest – the north not only has less to see but is also dogged by tribalism. The Queen Elizabeth National Park is the classic safari experience, with elephants, lions, leopards, buffalo, antelope and hyena. I’d been to East Africa before, but somehow Uganda felt different. It was awesome and diverse, but also oddly calm, greener, more lush – I didn’t feel I as though was treading a well-worn safari route.

From the classic to something different, we went to Kibale National Park to track, on foot, the habituated chimpanzees that live there. It’s a relatively flat and easy walk, provided the chimps aren’t up to much – the ones we followed were charging around in search of food, causing us to work up quite a sweat! We also spotted some red colobus monkeys, just one of the impressive 13 primate species living there. From my campsite outside the park that evening, looking out across the treetops, I could hear the hoots of the chimps. It was a sound to truly stir the soul.

The easiest way to enjoy the scenery and the wildlife in Uganda is by boat, especially on the Kazinga Channel that links the stunning lakes Edward and George. What sights we savoured: buffalo and hippos clustered along the cool water’s edge; crocodiles sunbathing on the shore; weaverbird nests hanging like lanterns from the overhanging trees; kingfishers, storks and muscular sea eagles that even this urban non-birder could identify; crested cranes, the national bird, strutting along the sand twitching their crowns.

The jewel in Uganda’s wildlife crown is the Bwindi Impenetrable Forest, where half the world’s wild mountain gorillas live. This is a big deal, as one can only see these endangered apes in Uganda, Rwanda and, should you be so brave, the Democratic Republic of Congo. But it takes some effort: to get to one of the six gorilla families that live in Bwindi, you must climb steep slopes through dense thicket. Visitors’ permits are a sting at $500, allowing only one hour with the gorillas – albeit one of the most exhilarating hours possible. A seventh family group lives in the nearby bijou Mgahinga National Park, but check before going as its members sometimes wander across the border into Rwanda or the Democratic Republic of the Congo.

If you don’t want to see the gorillas, Bwindi is also a UNESCO world-heritage site and home to many other animals such as the black-and-white colobus, elephant and giant forest hog. The Harper’s Bazaar crowd head to Clouds Mountain Gorilla Lodge: 10 luxury stone cottages, each with a roaring fire for the forest’s cool nights, along with a library and botanical garden.

Ugandans have to work hard to survive (at present they can only expect to live to 53), yet I was struck by their warm welcome. They are fantastically friendly, and when people ask how you are, they generally mean it – it’s not merely an introduction in order to sell you something. And if you do go shopping, prepare to haggle in curio shops but spare yourself the embarrassment of being ignored if you try bartering for bananas at the market. As we drove around we saw women in the traditional dress of colourful floor-length skirts and puff-sleeved tops; most men, by contrast, wear collared shirts and even suits. It is generally speaking pretty safe, but as with many African countries the biggest threats are malaria and bad driving – we took a local matatu (shared taxi) that was driven like a getaway car.

Some visitors take a break from the wildlife to hike, for which there is no better place than the Rwenzori Mountains, the tallest mountain range in Africa. You can hike among its peaks for one day or several, up to a height of around 5,000 metres if you’re super-fit. It is the glacial water from these mountains that feeds Lakes Edward and George.

From serious effort to serious relaxation, every trip to Uganda should include a stop at Lake Bunyoni. The name means ‘place of little birds’, and, despite a bone-jangling drive up to 1,840 metres above sea level, you can see why they come here. This is 60 square kilometres of sparkling freshwater – free of bilharzia, a chronic parasitic disease common throughout Africa – and the continent’s second deepest lake. It is hemmed in by steep hills, all drenched in the same bright green and punched through with bursts of pink and purple flowers. There is plenty of accommodation to choose from, and you can rent a lake-facing tent with wooden porch and floor, proper beds and warm blankets for just $20. Canoes are available, but I just jumped in. Only one species of fish lives in the cool waters, along with some crayfish. The only other thing to do here is sit by the fire at the open-air bar and watch the sun set over the water, then later sample local and moreish dishes such as matoke (mashed plantain) and rolex (an omelette-filled chapati unique to Uganda).

We finished our Ugandan exploration in Jinja, just east of the capital and fast becoming the adrenaline-centre of Africa. It’s a do-able day-trip to take on grade-five rapids or bungee jumps – or, like me, watch it all from the comfort of an awesome cliff-top bar. This is the source of the Nile, and water thunders north from here until a bottleneck at the magnificent Murchison Falls, themselves situated in Uganda’s biggest national park of the same name. Could they make it any easier?

Back in Kampala, as I waited for my taxi to the airport, I thought about how Uganda really is a ‘pearl’ that only a lucky few have seen. Perhaps you should go and discover it for yourself.