Before Marilyn Monroe donned a sparkling sheer dress to sing “Happy Birthday, Mr. President” to John F. Kennedy in 1962, she wore a similarly scandalous ensemble to meet the queen.

It was 1956, and a 30-year-old Monroe was in London filming a fizzy romantic comedy, “The Prince and the Showgirl,” when she got an invite to attend a Royal Command Performance of the new movie “The Battle of the River Plate,” and shake hands with Queen Elizabeth II.

But according to Michelle Morgan’s “When Marilyn Met the Queen” (Pegasus Books), out now, Monroe ignored the officials’ pleas to dress conservatively. Instead, she chose a skin-tight gold lamé gown that was “so low-cut that the tops of [her] breasts were on full display.”

Cameras flashed, fans screamed and men stared. One attendee, singer Jane Morgan, sniffed, “Miss Monroe must have a terrible inferiority complex to dress the way she does.”

But for Monroe, the event was the highlight of her dreary four months in England — otherwise marked by a grueling shoot, crippling depression, the dissolution of her new production company and a drug overdose. Meeting Her Majesty, the actress said, was “the biggest thrill.”

Monroe had high hopes for her trip. “The Prince and the Showgirl” was the first movie the star actress would produce under Marilyn Monroe Productions, started out of her frustration with all the “dumb blonde” parts her studio kept giving her. She had hand-selected esteemed thespian Lawrence Olivier as her director and co-star. And she looked forward to a honeymoon of sorts with her new husband, playwright Arthur Miller, whom she brought along for the trip.

Yet Olivier condescended to her — explaining to the rest of the theater-trained cast that Monroe’s method-acting “technique was vastly different” and that “it would take her a while to get used to the way they worked.”

Morgan writes that his “snobbish attitude shocked [Monroe],” and the actress, known for her stage fright, would repeatedly flub her lines, delay going to set and sometimes refuse to come out of her dressing room. The servants at the estate where she stayed with Miller sold stories about them to the press. At one point, Monroe — addicted to sleeping and weight-loss pills — was rushed to the hospital early one morning, after a suspected drug overdose. (She missed three days of filming but then went back to work.)

As an escape, Monroe fantasized about meeting Queen Elizabeth.

The actress adopted Her Majesty’s favorite brands, buying gloves from Cornelia James and even swapping her beloved Chanel No. 5 for the queen’s preferred Yardley’s Lavender. “Her dream was to have tea at Buckingham Palace, and publicist Alan Arnold found the request on his daily to-do list,” Morgan writes.

When she finally received an invite for the Royal Command Performance, she spent every free moment she had practicing her curtsy and planning her outfit — a very low-cut gold gown with spaghetti straps and a matching cape. The day of the event, Oct. 29, she didn’t even show up on the set of her film.

Instead, she had her hair and makeup done and then — with the help of “several staff” — squeezed into her custom sexy lamé dress. She then slipped on long gloves and platform sandals, spritzed perfume and climbed into the car with her husband and her co-producer, Milton H. Greene.

“As the chauffeur pulled up outside London’s Empire Theater, it was as though the entire population of Britain was gathered outside,” Morgan writes. Monroe “smiled broadly, then threw back her cape to reveal her spectacular dress.” The photographers went wild. She and Miller joined the other celebrities — including Joan Crawford, Brigitte Bardot and Anika Ekberg — in line to greet the queen.

Elizabeth, in a “black, full-skirted gown and a diamond-and-emerald tiara,” briefly looked Monroe “up and down” as the nervous actress took her hand and curtsied. The two “chatted for several minutes” about the bicycle rides Monroe and Miller enjoyed taking near Windsor Castle. Monroe then spoke with Princess Margaret about “cycling, life in England and the making of ‘The Sleeping Prince,’ before the Hollywood star urged the princess to go see her husband’s new play, “A View from the Bridge,” in London. “The princess laughed and said she might,” Monroe recalled afterwards.

It was, for Monroe, an unforgettable evening. “The Queen is very warm-hearted,” Monroe told journalists. “She radiates sweetness.”

And while the press, the royal officials and Monroe’s fellow actors expressed dismay at Monroe’s revealing gown that upstaged the queen and her sister, Elizabeth herself didn’t seem to notice.

“I thought Miss Monroe was a very sweet person,” Her Majesty told a friend. “But I felt sorry for her, because she was so nervous that she had licked all her lipstick off.”