Anguilla. Why, our writer asks himself, would an accessible little island in the British West Indies with a surfeit of world-class beaches remain so unknown to the traveling public?

IT was a gray stormy day in the West Indies, but even from the rain-blurred window of the 9-seat Britten-Norman Islander there was no hiding Anguilla's No. 1 asset: beaches. ``That's Shoal Bay,'' said a young Anguillan in the seat behind me, indicating a gorgeous stretch of white sand. ``It's our most beautiful beach. Ask anyone.'' I did, and although most of those I polled in the days ahead put Shoal Bay first, there were also votes for Captains Bay, Savanna Bay, Maundays Bay, Long Bay, and Meads Bay. I think Alan Gumbs, a local hotelier and raconteur who has seen a lot of the Caribbean, put the issue in perspective when he declared to me on my first afternoon: ``Conservatively speaking, Anguilla [pronounced an-GWIL-a] has five of the 10 most beautiful beaches in the world.''

Maybe he was trying to take my mind off the weather (which turned perfect a day later), but what he did was to arouse the fascination of a lifelong buff. As I made the rounds sampling Anguilla's matchless shoreline I also began to ask myself why a perfectly accessible island with a surfeit of world-class beaches can remain so unknown to the wandering public.

One ready answer, I suppose, is purely geological. In a sea of high, green, alluring neighbors, Anguilla is a low, somewhat scrubby coral island with little of the lush vegetation that winter dreams are made of. Second, there isn't a lot to divert the restless tourist -- no golf courses, no tennis camps, no casinos, and until this winter, no posh resort hotels.

As of December, the Malliouhana Hotel lay smartly wedged between two of those all-star beaches, Meads Bay and Long Bay, on the northwest coast -- a touch of the C^ote d'Azur and the Bristol of Paris, its English developers hope. There are only 40 rooms, at $225 and up per day (including continental breakfast only), so the Malliouhana won't exactly bring a deluge. Yet one feels the island is bracing itself. It wants to avoid following the same path of its brassy neighbor to the east, St. Martin.

It seems only yesterday that St. Martin -- only 15 minutes away by water taxi and less by light plane -- dozed in an Anguilla-like innocence. If Anguilla has hope, it is in its historic resistance to outside influence. The island was discovered by Columbus who, fixing the long undulating form in his spyglass, called it Anguilla, eel in Spanish. In the ensuing five centuries its modest topography as much as anything else helped to keep it fresh of spirit and unsullied by foreign interests.

Although the British colonized the island, they could see it lacked the fertility and rainfall to introduce sugar planting. Without a plantation society, there was no slavery. Anguilla was settled by runaways and, later, by emancipated slaves and a scattering of Irish men fleeing Cromwell. From the start the people owned the land, fished the waters, grew patches of pigeon peas, corn, and tomatoes, and sailed their colorful yachts. And they still do.

Anguilla was even briefly on Page 1 of the world's press. That was in the late 1960s when, drifting toward independence with its British colonial neighbors Nevis and St. Kitts, but fearing domination in a three-way pact, Anguilla quietly rebelled. Under cover of night, British paratroopers and police landed to restore order. Today Anguilla governs itself internally while Whitehall runs its foreign affairs, an arrangement the islanders see as the best of both worlds. They drive on the left, fly the Union Jack (some of the most tattered flags you'll see), and watch while foreign developers eye the tempting beaches.

For now Anguilla remains reasonably undeveloped. Only a single stoplight has been installed, and it seems extraneous. Gas lamps were a fact of island life only a few years ago. Crime is almost nil. One morning at the Cinnamon Reef Hotel I overheard the manager and an employee discussing how to treat some culprits they'd just found on the property. It turned out they were talking about trespassing cows.

On an island 16 miles long and barely two miles wide at any point, the sea and those matchless beaches are never far away. At the sleepy little settlement of Sandy Ground I hired a fisherman named Raphael (Raffy) Edwards, who sometimes takes out snorkeling and scuba parties, to visit an offshore cay called Sandy Island. We buzzed out to that dream-looking atoll in Raffy's wooden outboard Skylab, but when we arrived we found the cay staked out by a grilled-seafood operation and visited by a catamaran load of snorkelers from St. Martin.

From them on, I resolved to stay closer to shore. On Anguilla you don't need to go hunting for new beaches. Shoal Bay, true to its billing, was a winner. It's the favorite destination of day trippers who come over by ferry from St. Martin. The long curving pinkish white strand is perfect for strolling, reclining, or flapping about the shallows with mask and fins. Protectors of the island's ecology are already worried about the arrival of a beachfront inn and a thatched caf'e called Happy Jack's, but believe me, when the day trippers are headed back to St. Martin in the afternoon, the beach is yours.

I also liked Captains Bay for its wild and remote location on the northeast coast; Savanna Bay for its encircling row of palms (rare for some reason on Anguilla); Long and Meads, which bracket the Malliouhana, for their almost symmetrical perfection, and Rendezvous for its never-ending shells. I could go on, but you get the point. Sand is still Anguilla's most endearing product.