In the early morning sunlight, a chicken strolls between the elegant sun loungers at the pool of the brand new Zemi Beach House resort on Anguilla, summing up how this quaint Caribbean island uniquely combines the rustic with the sophisticated.

Virtually unknown to tourists until the 1980s, tiny Anguilla, only 35 square miles (and only three miles at its widest point), has become a magnet for celebrities drawn by its private beaches and secret islands far from the prying eyes of the paparazzi.

But it still manages to retain the simplicity of the old-fashioned Caribbean. Here you are as likely to be heading to the beach with Justin Bieber as you are a herd of goats, a green iguana or a family of ducks.

But A list or D list, people don't come here for the glitz found on Anguilla's more developed neighbours. There are no chain hotels here, no all –inclusives, no casinos or fast food outlets. Even jet-skis are not allowed.

Instead, expect to find rickety beach bars enjoyed by locals and visitors alike, driftwood signs pointing to secluded bays, dusty roads, roadside food stalls and traditional brightly painted houses.

Getting thereFly: Flights to Antiqua start from £617. Fly via Paris with Air France to St Martin and then take the ferry to Anguilla www.funtime-charters.com Or fly to Antigua with BA.com Liat have now introduced a daily connection flight from Antigua to Anguilla which starts from $269 (£189) return www.liat.com Stay: Zemi Beach. Delux rooms start from $699 (£491) with breakfast. zemibeach.com (see review) more info: www.ivisitanguilla.com

The low-key capital is called simply "The Valley" and is no bigger than a village.

Despite its sleepy ambience, Anguilla has a colourful history. Colonised by Britain in 1650, its terrain and climate made sugar difficult to grow, so the plantation system never worked here.

In 1967 opposition to including Anguilla in an associated state administered by St Kitts culminated in the 'bloodless revolution.' Saint Kitts and Nevis gained full independence from Britain in 1983, but Anguilla, happily, remains a British overseas territory.

Today the Anguillan economy has grown and the nation is also recognized as a world class tax haven, with no taxes on either personal or corporate income.

To learn more about its past, it's worth visiting the Heritage Museum run by local historian and personality Colville Perry, who has stuffed the small building with photographs, objects and curios and is usually on hand to tell the island's stories to visitors.

Though it exudes a sense of unworldliness, Anguilla has earned the title of the cuisine capital of the Caribbean and has a lively food scene - there are literally hundreds of eating places. These range from fine dining upmarket restaurants to simple shacks selling fruit and vegetables to eat on the fly or Ken's BBQ on The Strip in The Valley, selling fresh fish and local specialities.

You can enjoy a real Robinson Crusoe experience by getting marooned on one of the cays such as Sandy Island or Scilly Cay which you can see from the dock. If you wave frantically enough they send over a ferry to pick you up. Spend the day snorkelling, relaxing and enjoying fresh fish and rum punch from the beach bar. There's also Prickly Pear Cay, one of six marine protected areas. It's around six miles north of Anguilla where the Yacht Regatta takes place in May each year. If you have sea legs, sailing is a lovely way to explore. You can hire a sloop - a one-masted sailing boat - from Tradition charters or join one of their excursions.

The lush landscape is hemmed by 33 beautiful beaches, so time out enjoying the sun and sand is a must. The best two beaches are Rendezvous Bay with endless beach bars or the tucked-away Little Bay which is so discrete it is only accessible by boat or climbing down rocks. Early morning is the best time to see the ponds wetlands and birds such as egrets, plovers and terns.

But there's also the art of "liming" - a phrase used in the Caribbean that means chilling out. To find out how best to do it, seek out Bankie Banx, Anguilla's answer to Bob Dylan who can be found hanging out at the beachfront Dune bar, just down the beach from CusinArt hotel.

In any case, most bars and restaurants have live music and the strains of soca and calypso can be heard everywhere. There is a thriving music scene with festivals throughout the year, the most notable being the annual reggae festival, 'Moonsplash' in April.