Seen from the sky, Rodrigues is an extraordinary green, the land parcelled out into vegetable patches and fields of sweetcorn. The only place of any size is the capital Port Mathurin, a jumble of red corrugated roofs; as we prepare to land I spy the coral reef which completely surrounds the island.

Only 11 miles long and four miles wide, this tiny island is a short 90-minute hop from Mauritius — you can’t fly direct to Rodrigues from the UK as its airport only handles small ATR prop planes — and for now, international tourism has barely made an impact on the island.

Over half the visitors come from Mauritius, attracted by the beaches and the complete lack of development here. There is only a handful of upmarket hotels, and most of the accommodation is in small B&Bs with evocative names like La Belle Rodriguaise or Cases à Gardenias. Instead of soulless hotel restaurants, you sit down for dinner with the family and enjoy local Creole specialities.

I get an idea of what ingredients are on offer when I visit the Saturday market in Port Mathurin. Rows of stalls are selling the freshest of fruit and veg, together with small jars of the local spicy pickles. There’s a choice of mango, tamarind, star fruit and aubergine but I buy the piquant pounded chilli paste which turns up on restaurant tables everywhere.

Dried fish is heaped in silvery stacks and you can find the fresh variety just a few paces away at the small harbour, where fishermen sell their catch of the day.

A charming assortment of brightly painted shacks with tin roofs, the few elegant single storey colonial houses are set aside for the capital’s government offices. Even the tourist office occupies a wooden hut dating from 1897. Among the traditional buildings, the single large modern structure is home to the new regional assembly.

Outside the Saturday morning bustle, it’s a sleepy place. Buses, painted in garish colours, leave here at regular intervals to climb the steep winding road leading to the forested centre of the island

I head west out of town to visit the main tourist attraction on Rodrigues, the François Leguat Giant Tortoise and Cave Reserve. It’s named after a Huguenot exile who arrived here in 1691, with eight others, escaping persecution in France.

The island was then completely unoccupied, a paradise packed with giant tortoises and large flightless birds known as solitaires.

The settlers only lasted a couple of years before sailing back to Mauritius, perhaps because there were no women in the group. The tortoises were also soon gone, as they provided a supply of fresh meat for sailing ships on long voyages. And the solitaire went the same way as the more famous dodo on neighbouring Mauritius.

The reserve you can visit today was founded in 2007 and includes an interesting museum plus a collection of around 2,000 tortoises, split between the giant Aldabra variety and the smaller radiated tortoise. They’re certainly friendly, partial to having their necks tickled, and they roam the park’s 20 hectares in a landscape which has also been repopulated by scarce native plants.

Underground is a network of 11 caves, and the 500m Grande Caverne is open to visitors. A guide leads you along wooden walkways pointing out illuminated stalactites and stalagmites, formed over many thousands of years.

Even more fun is the Caverne Patate nearby, the longest on the island at over one kilometre long. There’s no electricity here and a guide takes you by torchlight on a subterranean slippery pathway, from one end to emerge at the other, blinking in the bright sunlight.

After all this darkness, I need some sun so head to the east of the island where delightful beaches lie in sunken coves, accessible only on foot. I start at St Francois, facing the broad sweep of Baie de l’Est, and walk for half an hour to the tiny Trou d’Argent.

Buried pirate treasure is reputed to lie under the sand, but I’m only interested in swimming and have the beach to myself. I continue, passing more sparkling sand at Grand Anse and Anse Bouteille, before reaching the tiny settlement of Graviers, nothing more than a handful of shacks.

Over the next couple of days I explore the rest of the island on a network of well-marked trails. I meet shepherds minding their goats or fishermen hauling their catch and occasionally stop to ask the way from women tending their vegetables.

Unlike Mauritius, there’s no sugarcane grown here, which explains why the people have African, rather than Indian features. In the 18th century, they were brought here as slaves from Madagascar and Mozambique to work on the land.

In the South East, I encounter a tribe of kite surfers, attracted by strong onshore winds and the shallow lagoon, but otherwise there are few tourists to be found.

What’s astonishing is that Rodrigues has managed to hold off the developers and preserve this beautiful part of the Indian Ocean. It can’t remain a secret for long.