The snake is harmless, but don’t touch it,’ said Veno, our local guide, pointing to the 2ft serpent slithering across the cave wall. ‘When it’s scared, its skin sends out a stinky liquid. You won’t be able to wash off the smell for a week.’

My son, Daniel, ten, and I were a mile and a half from daylight in Racer Cave, one of the many enormous underground networks in the Gunung Mulu national park in the Malaysian part of Borneo.

To reach the cavern in which we stood, a dark cathedral festooned with stalactites, had taken a little doing. The Mulu park covers more than 200 square miles: a protected enclave of rainforest, clear rivers and craggy mountains. The only ways to get there are by a day-long ride in a riverboat, or on one of the turbo-prop planes that serve its little airstrip, a grassy jungle clearing.

At the north-eastern end of the island, outside Kota Kinabalu, we got our orangutan sighting

That part of the journey, from the coast to the park’s headquarters, we’d accomplished two days earlier. From there, we travelled to the entrance of the cave in a flat-bottomed, motorised canoe. In places, the boatman had to use a pole as we navigated our way through shallows and up rapids.

The entrance was a rent at the bottom of a cliff face, half-hidden behind a screen of creepers. Then we had to squeeze through a narrow gap, climb down several vertical pits where we needed a rope, and romp along gigantic tunnels at least 100ft high. Besides the snakes, we passed hand-sized spiders, their eyes sparkling under our headlamps, and giant crickets, their antennae 10in long.

When we finally turned round – still miles from the cave’s furthest reaches – we felt remote. However, our base for this and other Mulu adventures was more than comfortable: the Royal Mulu Resort. We knew that when we emerged, we would be returning to spacious, air-conditioned rooms, marble bathrooms, a swimming pool and a restaurant with a decent wine list.

To reach the cavern in which we stood, a dark cathedral festooned with stalactites, had taken a little doing

Besides the cave, there was another unforgettable Mulu highlight: a walk with Veno through the noisome jungle at night. Using a laser pointer, he picked out creatures we would otherwise have missed, including big, plump tree frogs and stick insects 2ft long.

Our three days in Mulu came almost at the end of a family holiday (taking a break from caving that day were my arachnophobe wife, Carolyn, and elder son Jacob, 15). In three weeks, we visited not only Borneo but some of West Malaysia.

At the end of it all there could be only one verdict. This is a fantastic destination, endowed with diverse natural wonders. It also has a well-developed tourist infrastructure, with low-cost internal flights, and resort hotels to equal any in the world.

Before the trip, we were worried about the climate. But although we went in August and were almost on the Equator, the weather was never oppressively hot, usually below 30C. Britain’s summer is also Malaysia’s ‘Arab season’, when tourists from the furnaces of the Arabian peninsula come for the relative cool.

The local travel firm Borneo Adventure took us on an atmospheric trip by kayak down a rainforest river

We started in Singapore, a futuristic metropolis that was the perfect place to recover from the 13-hour flight from London. Taking advantage of the ‘Singapore Stopover’ package offered by Singapore Airlines, which covers accommodation and entry to the city’s major attractions, we stayed at the original Shangri-La, the base of the hotel chain with 84 branches across Asia and beyond.

Around the corner were the designer-label stores of Orchard Road. But there is more to Singapore than shopping. At the Marina, on the shores of the Straits, two huge transparent pavilions house the Gardens on the Bay – a little like Cornwall’s Eden Project, but more spectacular. In one of the domes, thousands of orchids flourish in an artificial ‘cloud forest’, sustained by a 100ft indoor waterfall. The night zoo was also unmissable – we picked our way through the moonlight within a few feet of dozing leopards and frisky young elephants.

From Singapore, a short flight brought us to Penang, our first stop in Malaysia. Down by the sea at George Town, and on the forested hills above, careful conservation has preserved the architectural splendour of the British colonial period. This is why Channel 4 chose to shoot its drama Indian Summers, a historical series about the last years of the Raj, in Penang rather than Indian Simla, where the story is set. In Simla, there has been too much new construction.

The drama Indian Summers was shot in Penang, where careful conservation had preserved the colonial past

But colonialism has little relevance to Penang today. A pulsating island of 1.5 million people, this is ‘rising Asia’ exemplified, with gleaming malls and apartment blocks, raucous night markets and incredible food.

Awarded the accolade as 2014’s top foodie destination by Lonely Planet, Penang has more than its share of excellent, cheap restaurants. However, what makes it different is the quality of its ‘hawker food’, served from roadside trucks and in open-air plazas, with stalls that offer thousands of variants on noodles, rice, every kind of meat, fish, seafood and spices.

Our next destination, Langkawi, is also an island, but very different from Penang: instead it is a sparsely populated paradise of white-sand beaches and mangroves.

Down by the sea at George Town, and on the forested hills above Penang, careful conservation has preserved the architectural splendour of the British colonial period

We took a boat deep into its waterways and were rewarded with close-up views of proboscis monkeys and dozens of majestic eagles, diving into the teeming waters for their lunch.

We stayed at the Pelangi Beach, a tasteful, low-rise complex of darkwood cabins, pools and restaurants. It is a popular spot for honeymooners. Stroll along the beach with the rustling palms silhouetted against a blazing tropical sunset, and it’s easy to see why.

Next it was time for Borneo. Before Mulu, we stayed in Kuching, a relaxed and charming city that is capital of the state of Sarawak. We were guests at the home of Philip Yong, proprietor of the local travel firm Borneo Adventure, which took us on an atmospheric trip by kayak down a rainforest river and an attempt to see orangutans at a primate reserve.

This was unsuccessful: August is the height of Borneo’s ‘fruiting season’, when the trees are laden with every kind of tropical goodie – this meant the apes had no interest in collecting their food from the reserve’s wardens, under the eyes of tourists.

Taking advantage of the ‘Singapore Stopover’ package offered by Singapore Airlines, which covers accommodation and entry to the city’s major attractions, we stayed at the original Shangri-La resort

A few days later, however, at the north-eastern end of the island outside Kota Kinabalu – or KK, as it is usually known – we got our orangutan sighting. A bulky paterfamilias lurked warily in the background while two adolescent males gambolled about for the best part of an hour, racing up tree trunks and peeling fruit while hanging from creepers by their toes.

Our home in KK for six nights was the Tanjung Aru, another Shangri-La outpost. It helped that our rooms had one of the finest views I’ve seen, across the glassy South China Sea to the islands of the Tunku Abdul Rahman marine park. A 15-minute speedboat ride from the hotel jetty, the islands offer exquisite reef snorkelling. Want to find Nemo and dozens of other marine species besides, swimming amid the living, multi-coloured coral? This is your chance.

Like the other resorts in which we stayed, the Tanjung Aru carries on an estimable tradition: free cocktails and delicious snacks in its clubroom, a perfect place to watch the sun go down.

There’s a lot to Malaysia we didn’t have time to see. But this is an alluring and beautiful country. With any luck, we’ll be back.

We stayed at the Pelangi Beach, a tasteful, low-rise complex of darkwood cabins, pools and restaurants