We are in the densely forested ghut, or ravine, that adjoins the landscaped gardens of the Ottley’s Plantation Inn. Mysterious signposts to “the tree” send us deeper into the woods, where there are indeed many fine trees, monkeys scampering in their branches above our heads. After several pauses to wonder if this or that towering, creeper-garlanded specimen is “the tree” ... we literally stop in our tracks. And stare. This has to be it.

Imagine something dreamt up by JK Rowling in cahoots with Antoni Gaudi: a great cataract of foot-high root ridges runs down the slopes of the ghut from a complex multi-stranded “trunk” that shoots dense branches skywards. We climb inside the hollow trunk, into the vast space occupied by the original “host tree” before the unstoppable rampage of this strangler fig killed it off, shooting out the aerial roots that now course like a frozen waterfall down the valley. And the whole process has probably taken only about 75 years.

There are Caribbean islands for the glitz and glamour of large modern hotels and purpose-built resorts. But for close encounters with the natural glories of the real Caribbean, head for the small island of St Kitts — and its even tinier sister Nevis — an even more inviting destination since regular direct flights from the UK mean you can avoid the hell of a transfer in Antigua's horrible airport.

Stay in comfortable converted plantation houses — Ottley’s rooms are bungalows in the grounds with sea views. Rawlins Plantation Inn grows 20 different tropical fruits on its land and serves a legendary Sunday buffet with moreish local delicacy the johnny cake, a light-as-air cross between a chappati and a Yorkshire pudding.

A leisurely tour round St Kitts doesn’t take long and quickly reveals the essentials of its history: Europeans wiped out the native Caribs — and introduced the first of the now ubiquitous monkeys; African slaves, auctioned in capital Basse Terre’s deceptively pretty main square, worked on the sugar plantations and built the massive Fort Brimstone, the biggest military complex in the Americas, for the British army. Indpendence came in 1983 and the sugar industry finally ground to a halt in 2005.

It’s the Caribbean, so you can, of course, just go to the beach. But if you want something more active, trek up mount Liamuiga, at 3,792ft the highest point in the Lesser Antilles. The guided clamber (from £45 with rogers rainforesttours.com) through dense forest is steep and tricky over damp roots and stones, up and up till you look over a ridge and behold what you can already smell: 400ft below is the sulphurous pool in the mouth of the volcano — last active 450 years ago.

Visitors have to wait till nightfall for the best natural encounter of all, joining the marine biologists who are battling to keep Cayon to Keys beach safe for leatherback turtles. Every night, from March to July, they wait in the dark for the 1,200lb, 5ft long females to come ashore to dig a hole into which they lay up to 90 white eggs, from baby mozzarella to billiard ball in size. Tourists are encouraged to help by counting the eggs. The biologists measure and tag and sometimes guide the mother back to the sea, and away from the street lights beyond the road that can look like moonlight off the water. The group tries hard to educate the islanders on turtle conservation, working with former fishermen to spread the word (stkittsturtles.com).

Over on Nevis, if you can take the heat you can join the local matriarchs who bathe in the same (extremely) hot springs that soothed Nelson’s aches and pains more than 200 years ago, and sip poolside cocktails in the elegant and welcoming Montpelier Plantation, a member of the Relais & Chateaux group. But try to fit in a snorkelling outing with marine biologist Barbara Whitman at Oualie beach, after an instructive session with the sea life in her tiny home-made aquarium (£35, undertheseanevis.com).

And keep up, if you can, with Jim Johnson on a rainforest trek (two hours, £12, walknevis.com). His encyclopaedic knowledge of local plants, includes the poisonous ones that render you temporarily speechless, and the seeds that kill you stone dead. After that, you’ll need a Killer Bee: not more fearsome wildlife — it’s the rum punch at Sunshine’s bar on Pinney’s Beach.

BA flights to St Kitts depart Gatwick on Saturdays and, from March 30, Tuesdays. Seven nights B&B at Ottley’s Plantation Inn from £1,039pp or seven nights at Montpelier Plantation from £1,399, including flights (0844 493 0758, ba.com/stkitts)

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