Agatha Christie Country : Burgh Island is the perfect place for a Mystery writer to set a murder, for a king to have a secret rendezvous, for a pirate to bury treasure. . .

Walking amid the rare pyramidal orchards that dot the lush grass on this island, all you can hear are the cries of the sea gulls and the waves crashing against the rocks.

A gale has since blown away the gazebo that overlooked the natural, seawater swimming pool, and all that remains of St. Michael’s Chapel--said to be the haunt of 15th-Century English smugglers--are the original walls.

Burgh Island is, you might say, the perfect place for a murder.

Agatha Christie thought so. She wrote parts of two of her most famous novels, “Evil Under the Sun” and “And Then There Were None,” in that once-upon-a-time gazebo above Mermaid Pool. The nearby Bluefin Cove, which is better known to Christie fans as Pixie Cove, is where poor Arlene Stuart Marshall was strangled to death.

As if to secure the island’s place in whodunit history, Christie immortalized it by printing a map of Burgh Island in “Evil Under the Sun.”

In September the mystery writer’s daughter, Rosalind Hicks, came to the island to help plan a luncheon/fund-raiser for the Agatha Christie Memorial Room in Tor Abbey, a few miles from where the author lived much of her life.

The island isn’t an island at all when low tides link it to the mainland via a 300-yard footpath. And the pool isn’t even a pool during those same tides. When the tide swirls back every six hours, a sea tractor with wheels as tall as the waves trundles forth to ferry guests to and from nearby Bigbury-on-Sea.

It’s probably its mysterious dichotomy that has made this is-and-isn’t island off the south coast of Devon such an attraction for generations of Britons. There are even two sides to its size. One of the owners says it’s 26 acres, the other claims it’s 24.

The island also has a romantic claim to fame. Two of its most celebrated guests, the Duke and Duchess of Windsor, used the Burgh Island Hotel as a hideaway during the days before his abdication, when he was still King Edward VIII and she was Wallis Simpson.

Before the Windsors and Noel Coward, who visited the island frequently, there was the infamous Tom Crocker, the 14th-Century pirate who first made Burgh a treasure trove. His ghost is said to visit the island’s 640-year-old pub, Ye Olde Pilchard Inn, where his hook-nosed profile is cut into the stone fireplace.

The Pilchard is believed to be one of the oldest fully licensed (for serving liquor) premises in the kingdom, having been built around 1346 and restored in 1913. Its whitewashed, thick stone walls are set close against the edge of the sea, and it is filled with authentic ship artifacts. The Pilchard is a favorite pub of locals intent upon a pint of ale or a plowman’s lunch. When the tide is low, people walk across the sand in droves just to drink the Pilchard’s curiously strong “real ale.”

There, on any given day or night, except for high tides when he drives the 20-year-old tractor, you will find Jimbo, everyone’s favorite islander. When things get really busy at the inn, Jimbo has been known to pull pints in the pub. Usually, he drinks them. He is also on record as saying he’s had a bad year if he has to buy himself more than three pints a season.

The Pilchard also houses a small bistro that serves simple meals centering around the catch of the day--lobster, crab, bass, mackerel, herring, plaice or pilchard--depending on the season.

The island’s real crown jewel is the hotel, built in 1929 by the founder of the company that owned London’s Comedy Theater, where Agatha Christie’s plays were performed. The once-splendid Art Deco hostelry had fallen upon hard times and become a rather tacky time-share complex.

Enter Beatrice and Tony Porter, who saw the island for the first time last November, fell in love with it and within weeks sold their home in London, their Jaguar, their boat and withdrew their life savings to buy the island.

For an original investment of just over 500,000 (about $754,000) and months of 18- and 20-hour days, the former fashion consultants have restored much of the hotel to its former glory.

Bea describes the hotel as a seaside sanctuary that’s especially thrilling to those who’d like to relive the bright young things era of the ‘30s. Tony thinks the hotel looks like an ocean liner moving silently and smoothly on a transatlantic mission called the Great Escape.

Particularly Appropriate

His allusion to a ship is particularly appropriate. Part of the hotel was once the top deck of a ship’s stern--possibly the captain’s quarters. That ship, the Ganges, was the last sail-powered vessel commissioned in the Royal Navy. It served as a training ship until it broke up about 50 years ago.

Right now the Ganges Bar is still waiting to become shipshape as the Porters continue their careful restoration. Already, members of the Ganges Society, whose aim it is to find, admire and note all the bits of memorabilia associated with the ship, are planning a reunion at the hotel sometime early in 1987.

The Porters are long-time Art Deco collectors, and their home in London was something of a shrine to that period. Their own Art Deco finds fit somewhat miraculously into the hotel’s Palm Court and the 36-foot ballroom.

Their restoration is so authentic that there is something of a time warp about the place. The oak and teak parquet flooring in the Palm Court and the terrazzo floor of the adjacent Sun Lounge are genuine ‘30s. So too are the fan-topped radiators, the vanitory tables and lamps in the ladies room and the original Lloyd Loom wicker chairs in the Palm Court. Even the lift has been uplifted.

The hotel’s private rooms all have been gutted and renovated and now are 13 luxury suites, each with sitting room, state-of-art kitchenette, bathroom and either one or two bedrooms decorated in ‘30s shades of pastel blue, green, pink or gray. All but four have balconies. All have a seaside view. Cupboards and furniture were made locally of solid beech.

While the hotel maintains its ‘30s sensibility, it has such ‘80s conveniences as color TV sets, central heating and constant hot water. There are free automatic laundry machines in the basement, a shop that sells everything from locally caught fish to wine, a children’s room with TV and videos (tapes include movies from the ‘30s) and a giant snooker table.

No Room Service, Restaurant

Just as the island is not always an island and the swimming pool is not always a swimming pool, the Burgh Island Hotel is not really a hotel. It has no room service and no restaurant, but continental breakfast is offered in the Sun Lounge, morning coffee and cocktails in the Palm Court and a proper English high tea, complete with scones and Devonshire clotted cream, again in the Sun Lounge.

Guests can cook in their rooms or, on fine evenings, choose their own lobster, fish, steak or chop, then grill it and eat on the terrace. Sometimes Bea cooks for everyone, as the spirit moves her.

Suites range in price per person per week from 62.50 (about $95) to 108.33 (about $163), depending on the season and the size of the suite. Two of the suites can accommodate six persons, seven can accommodate four and four suites can accommodate two or three. There is no service charge, and value added tax is included. Maid service at a daily rate of 2.50 (about $3.77) is optional.

So what do you do on this island paradise where the Atlantic Ocean flows through the western approaches on the way to the English Channel?

For one thing, you can have your choice of swimming in a western sea or an eastern sea because this tiny isthmus is where the tides meet from east and west.

When the tides part for six hours there appears, as if by magic, a stretch of golden beach that is a veritable sand box for castle builders and the pail-and-bucket brigade. Then, as the tides creep back and the beach shrinks, you can windsurf or fly a kite.

After a while you might want to retreat to dry land to walk the cliffs and climb the rocks or sunbathe in one of the secluded coves.

Favorite Footpath

A favorite footpath leads to the attached Little Island bird sanctuary, where you can sit for hours watching the puffins and sandpipers, the gannets and oyster catchers, the shags and guillemots.

The best walk is to the summit about 200 feet above sea level, where the heart-stopping view of the sea is interrupted by the rolling meadows of the Devon countryside, where black-faced sheep bleat to the beat of the waves.

If this sounds a little too contemplative, there’s tennis during the day and ballroom dancing at night. And on the mainland there’s Bigbury’s Championship Golf Course.

The mainland?

Tony calls it going across to England.

Where’s Burgh Island, then?

“This is another country,” Bea answers.

Burgh Island is a four-hour drive from London, a three-hour train ride from London’s Paddington Station to Plymouth or a one-hour flight from Heathrow Airport to Plymouth on Byron Airlines. Plymouth is 18 miles from Burgh Island and taxi drivers love the scenic route.

For reservations write to Burgh Island, Bigbury-on-Sea, South Devon TQ7 4AU, England or phone (0548) 810514.