A spluttering, guttural growl startles me early in the morning, but I'm relieved to discover it's not being generated by the stern-faced silverback looming two metres from my face.

Espresso machines have been whirring almost constantly since Gorilla Conservation Cafe opened in Entebbe last year, serving coffee farmed close to Uganda's prime mountain gorilla habitat.

"Kanyongi was one of my favourites," explains project founder Dr Gladys Kalema-Zikusoka, as she stares up at a black and white mural of the great ape who also features on 500g bags of the arabica beans, which are purchased from farmers in Bwindi at a fair, fixed price.

A Ugandan veterinarian and modern day Dian Fossey, she set up the social enterprise as part of her successful NGO Conservation Through Public Health, with a view to improving relations between the local community and wildlife on their doorstep. A portion of product sales is also donated to gorilla conservation.

Being a member of the Mubare (or M-group), the first habituated gorilla group in Uganda to be introduced to tourism 25 years ago this month, Kanyongi is a fitting mascot for the company.

"I knew him since he was born 20 years ago," recalls Gladys fondly. "He was a playful silverback who always liked interacting with tourists."

Sadly, Kanyongi died earlier this year following a fight with a rival silverback, but his legacy continues - in both the cups of steaming espresso brewed in Entebbe and the continuing success of gorilla tourism in this East African country.

Trekking gorillas in Bwindi

Along with neighbouring Rwanda and the DRC, Uganda is home to the world's population of mountain gorillas. At last count, in 2011, numbers were estimated to be 880 - although a new census, currently taking place, is likely to see that figure rise.

There are seven habituated troops living within Uganda's borders, and with permit prices temporarily frozen at US$600 (less than a half of the cost in Rwanda) tourism numbers are increasing, too.

I'm staying at Bwindi Lodge, where eight individual bandas (thatched cottages) tumble down the hillside, in a steep-rising forest that peaks and troughs like a stormy ocean. Even from bedroom windows, it's possible to touch the spindly white barks where hornbills swoop and red colobus monkeys scamper.

A winding path forms a green tunnel around the property and slopes alongside a river where, I'm told, one gorilla troop crossed only last week. "They were here for several hours," explains my gentle, attentive butler, who wakes me every morning with coffee, biscuits and a song.

Unfortunately, I need to travel a little further for my one-hour gorilla encounter. Leaving town, we drive for 45 minutes, passing women stoking mud bricks in kilns the size of temples and men on tea plantations stooping beneath the weight of heavily-laden baskets.

Vibrant, earthy, radiant and calm - the landscape is a spectrum of greens that would exhaust the shades on a Pantone palette.

The terrain in Uganda has a reputation for being challenging, but I find our 90-minute trek surprisingly manageable; even when the silverback in charge of the Habinyanja group makes us run for our money, we manage to keep up.

Whether they're gnawing sticks of bamboo, shimmying up trees (Uganda's gorillas are famously arboreal) or meticulously grooming one another, spending time with gorillas is priceless.

Dr Gladys tells me even Prince William once revealed to her that seeing gorillas in the wild was top of his bucket list.

Our own encounter is both humorous and endearing; one hormone-pumped teenager swings from a branch to steal a ranger's cap, and two tussling, fluffy-haired toddlers elicit endless oohs and ahhs from our group of eight.

On the trail of chimps in Kibale

The comparisons with human behaviour are uncanny - but a much closer relative of ours can be found further north in Kibale National Park, where a troop of 120 chimps has been habituated for tourism.

"They feel emotion," explains our tracker Gerard Kirungi, a thin, drawn man who has been guiding since 1991. "When a member of the family dies, chimps stay with the body until it swells."

Gerard, who grew up 6km from here, recalls his dad building trenches to catch bush meat. Those activities ceased years ago and tourism has since become a key source of income; when Gerard 'retires' next year, he plans to develop a cultural centre educating visitors about his community's way of life.

Tracking chimps is rewarding, but it is also hard work; they have a habit of moving - at pace.

Using her forearms like pistons a female runs on her knuckles, leaving me caught in a tangle of thorns and spider webs. Looking round, her expression is fixed with a mild smile; it would be improper to anthropomorphise but I suspect she's sniggering with glee.

Like gorilla trekking, the experience lasts an hour, although it costs substantially less - just US$150 for a permit.

Sweating and panting, we're finally treated to a tender few minutes as two chimps groom each other on a fallen tree trunk. Their actions mimic each other, lifting legs and scratching armpits; lost in concentration, the primates are even more transfixed than us.

You can find big cats, too

So many travellers fly in and out of Uganda, seeking a safari elsewhere, but in addition to gorillas, the country also has a healthy big cat population.

Lake Mburo National Park, where British ex-pat Ralph Schenk and his wife, Suni, built the beautiful Mihingo Lodge 10 years ago, claims one of the highest leopard densities in Africa. And although you'll have a hard time finding predators in the scrubby, thorny bush, crowd-free drives through the park are a delight.

Built on a granite kopje (small hill), with an infinity pool overhanging a plateau, the tented camp is a welcome recharge stop between Entebbe and Bwindi. Even the view from my toilet is superb, and when I'm not spending time coasting across Lake Mburo in search of African fish eagles, I'm relaxing on my terrace, enjoying Africa's vast, untamed landscapes.

In Queen Elizabeth National Park, 42 lions roam the southern sector - all adept at climbing trees; a response to the large number of elephants once found in the park. Further north, I'm told, they've even learned to clamber up euphorbia candelabra cacti.

We spend hours looking for paws draped over the branches of broad, open-armed fig trees, but focusing solely on big game is a big mistake.

Elegant butterflies, garish agama lizards and acrobatic Angolan swallows are some of the many smaller species deserving attention. At the peaceful Ishasha Wilderness Camp, you don't have to go far; a riverside location brings all these things to my canvas door.

Because that's the real joy of Uganda; beyond the headline-grabbing wildlife acts, there's a place and people we should all get to know.

How to get there

Audley Travel (audleytravel.com/Uganda; 01993 838 575) offers a tailor-made 11-night trip to Uganda from £5,985 per person (based on two sharing). Price includes international flights from Heathrow with Kenya Airways, transfers and accommodation with most meals included. The price also includes a chimp tracking excursion, game drives, gorilla trekking and a boat ride on Lake Mburo, as well as all necessary wildlife-viewing permits.