Leonardo DiCaprio, Shakira and Harrison Ford are fans; Gérard Depardieu is a regular. Melanie Griffith, Antonio Banderas and Francis Ford Coppola toured the islands for a millennium sailing holiday. To an increasing number of celebrities seeking accessible seclusion, exclusivity and activity, Los Roques rock.

Ninety-four miles north of South America, washed by the same clear seas as Trinidad, Tobago, St Martin and St Kitts, Los Roques make up the Caribbean’s southernmost archipelago. Three-hundred pieces of land in a lagoon the size of Greater London, the islands feel exclusive even before you reach them.

Taxiing towards the runway at Caracas airport, I was on board a propeller plane with just 10 seats. Mine was where a co-pilot would normally have sat — in front of me, speedometers, altimeters and a dial for remaining kilometres. I was even given a job. Until the very final moment before takeoff, the pilot asked me to hold my door wide open. The plane was stuffy, and wind from the whirring propellers made for a welcome cabin breeze.

As we flew north, it quickly became clear what the stars see in the place. Looking down, it was as if a collection of islands within a tropical blue lagoon had had a second sea — a turquoise laminate — pressed upon them. Most would-be islands remained underwater, as though a child’s collage of a desert-island scene had been so good that his teacher had had the whole thing glazed over. Only the really determined made it through the shallow, glistening glass.

We landed on a sandy airstrip on Gran Roque — the only island within the archipelago with accommodation or anything approaching physical height. After collecting my bag from the plane’s boot, I walked the 90 seconds from runway to residence: Gran Roque, in common with all the islands, is all but transport-free. Two small trucks — one to deliver water and a second to take rubbish away — are the only petrol-driven vehicles allowed. There are no cars and no motorbikes, just the odd electric golf buggy. Not that there’s a golf course — the islands are far too chilled out for that.

The stars come to Los Roques for the sea, not the tee. Boats — sailing, fishing, diving and posing — are the be-all and end-all of the islands. Every night, mini-flotillas shelter in the calm waters between shores, gently rocking their passengers to sleep. The early morning brings the waterborne activity: fishing boats deliver their nightly catch, shuttles take tourists to other islands, yachts are rigged for another day’s cruising. More decrepit vessels bob in the swell, little more than resting craft for pelicans between raids: the birds periodically taking off to dive-bomb the water, targeting fishy prey with a precision military tacticians dream of.

The pelicans are an impressive sight, not least for their ability to hold firm despite a constant and powerful breeze. Though the islands are away from the Caribbean’s hurricane belt, strong trade winds are a perennial presence on Los Roques; tough for those trying to shelter under flapping sunshades, but great for those who sail.

SAILING AROUND Los Roques is like cruising Greece in miniature — island-hopping, with smaller islands and shorter hops. I spent 24 hours on a 51ft yacht, time enough to fly-fish for barracuda, snorkel alongside turtles and sail to three islands — Nordisqui, Celuisqui and Selesqui. The names are Spanish phonetic versions of the English originals — Northeast Cay, St Louis Cay and Sailors Cay. It’s almost as if the Spanish cartographers, realising the islands’ star quality, set out to confuse a 16th-century posse of paparazzi.

Once you’ve had your fill of life on the water, it’s time to get under it. The diving here is superb: the sea is warm and clear, the coral phenomenal and the marine life prolific — turtles, rays and lobsters are common, whale sharks visit at times.

The most impressive activity of all, though, is kitesurfing — standing on a board while being pulled along at high speed by a canvas wing. The islands’ climate and geography are perfectly suited to the sport. Incidentally, the best kitesurfers in the world can jump entire islands. That’s how small some of these flecks of land are.

It’s superfluous to talk of main beaches or best sand here: almost every island has a beach running around its entire perimeter, making it easy to find a superb strip of sand all for yourself. With more than 300 islands in the group, there is often more than one per visitor outside peak periods. Some may be comically small, but this is a place where anyone can play Branson.

En route to one such island, the driver of my boat spotted another vessel coming the other way. In it were three men and five large, writhing lobsters. The former had free-dived for the latter minutes earlier. There seemed little point in waiting for the catch to reach land, so trade took place between the boats. Floating market. Deal done. Dinner sorted.

AWAY FROM the beach and the sea, pleasures are simpler. Down a side alley off Gran Roque’s painted-by-numbers main square, I came across a young boy fighting with a marlin. Not that the fish was the adversary. The boy was using the carcass of the creature like a knight uses a lance. I didn’t give him much hope. His competitor was brandishing a barracuda.