Poet Robert Burns knew that even the best-laid plans of mice and men can go awry. But not even Burns would have wished on a prince the kind of rotten luck that can wreck the best endeavors in war, peace or love. Fresh from his helicopter heroics in the Falklands campaign, Britain's dashing Prince Andrew, 22, had arranged a secret frolic in the Caribbean with a beautiful young companion. The couple sneaked quietly out of London, boarding the economy section of a British Airways jet as "Mr. and Mrs. A. Cambridge." Then, disaster. A photographer for the London Daily Express, traveling privately, recognized Andrew's toothy grin and messaged the scoop to deliriously happy editors back home. The Prince's date was swiftly identified as American-born soft-core actress Kathleen "Koo" Stark, 26, and the British press flew into a frenzy. Pictures of a nude and saucy Koo in lascivious poses were splashed over tabloid front pages. When the papers disclosed that Andrew had earlier taken Koo to meet his family at Balmoral, the Queen's Scottish castle, and possibly even introduced her to his mother, Buckingham Palace broke its embarrassed silence. "We do not know," said a spokesman frostily, "if the Queen was aware of the girl's acting career before she was invited to Balmoral."

Mercifully, Queen Elizabeth was not at home to read, over her morning cup of tea, such headlines as "SEX SCENE SIZZLERS FROM ANDY'S GIRL." Away in Australia on a duty tour with Prince Philip, however, she was reportedly distressed by Andrew's X-rated R&R. A member of her staff was quoted as saying, "It is one thing for a prince to be seen with a film actress, but quite another to go away on holiday with a blue movie star. The Queen feels badly let down."

Meanwhile, Prince Andrew was holed up on the tiny isle of Mustique in Princess Margaret's two-bedroom villa—barely a stone's throw from Mick Jagger's $1 million hideaway—where she used to tryst with former lover Roddy Llewellyn. There were four other persons in the party, including Andrew's detective and Koo's mother, retired TV hostess and actress Kathi Norris Caruso, of Venice, Fla. The rest of the two-square-mile isle was all but sinking under a gridlock of rapacious Fleet Street reporters and paparazzi. Two were arrested, allegedly for trespassing on the villa's 10-acre grounds. The couple rarely strayed beyond the compound, though anyone who saw them sailing, swimming or romping in the surf—she in a teeny bikini—was happy to relay it to reporters. Their candlelit dinners and video movies were private, but down at the island's sole saloon, Basil's Bar, the 15-piece calypso band was thumping out a new composition, The Randy Andy Mambo. Andrew slipped through the siege lines a few times, disguised by a false nose, dark glasses and a floppy hat, but the publicity was plainly flustering the Prince. His personal bodyguard was sent to give the press a plaintive message: "He feels he is on a well-deserved break after several months of active service and that now he is entitled just to enjoy himself and be left alone." Soon after, it was announced the Prince would cut short his vacation.

That was bad news for the great British public, which, unemployment notwithstanding, has not begrudged Andrew his royal caper. A poll in one newspaper reported majority support for the view that "if he wants to unwind with a shapely actress on a faraway island, good luck to him." There was a caveat, though: "But don't bring her home to Mum!"

The two met last February in the trendy London disco, Tramp, when Koo, supposedly unaware that she was addressing the Prince, asked Andrew and some noisy chums to pipe down. "Don't be boring," he shot back, then invited her to join him. When his ship, H.M.S. Invincible, returned last month, his first call reportedly was to Koo, a bit player with Britain's prestigious National Theater. By meeting discreetly, and by using a mutual friend, American writer Elizabeth Salomon, 27, as a beard on one occasion, the couple kept their dalliance secret until the Mustique Mustake. Koo's maid has since told reporters that she sometimes saw Andrew leaving the actress' apartment in London's swank Belgravia at 9 in the morning. In an aside which set TV newscasters around the world smirking, she added, "He looked very tired."

So who is Koo? The five-foot-five, dark-haired actress (nicknamed Koo as an infant; she used to coo at birds) was born in New York City, the youngest of three children of Hollywood TV and film producer Wilbur (The Thing) Stark and his wife, Kathi. A product of New York's upper-crust Miss Hewitt's School, she briefly attended the Professional Children's School and moved to London in 1970. Her first big break came in 1975 when, at 19, she landed the title role of a young nymphet in the blue movie Emily. The film featured Koo in a steamy lesbian love scene in a shower and two years later became Britain's biggest-earning soft-core film. Featured in PEOPLE's "Lookout" section in 1978, Stark explained that she didn't want to be "another Linda [Deep Throat] Lovelace. I do eventually want to be married with children." But she later made more blue movies. There were also bit parts in Star Wars and The Rocky Horror Picture Show. "I had to fake sex in my first film," she once admitted, "because I didn't know what it was like." (But she admits to losing her virginity at 17.)

If her career was stalled when she met Prince Andrew, it's stalled no more. Emily has received cable airings on Showtime, is being reissued as a movie, and video distributors have ordered 10,000 cassettes of the flick.

One royal family member apparently enjoying the respite from press scrutiny is Princess Diana. "I thought you'd all be in Mustique," she quipped last week to rain-soaked photographers. As for Andrew, his leave runs out October 18, and Buckingham Palace officials are doubtless hoping that the royal helicopter co-pilot will drop out of the headlines and get back on the flight line.