She always called him “Mr. President” — not Jack. He refused to kiss her on the lips when they made love. But Mimi Alford, a White House intern from New Jersey, was smitten nonetheless.

She was in the midst of an 18-month affair with the most powerful man in the world, sharing not only John F. Kennedy’s bed but also some of his darkest and most intimate moments.

In her explosive new tell-all, “Once Upon a Secret: My Affair with President John F. Kennedy and Its Aftermath,” Alford, now a 69-year-old grandmother and retired New York City church administrator, sets the record straight in searingly candid detail. The book, out Wednesday was bought by The Post at a Manhattan bookstore.

In the summer of 1962, Alford was a slender, golden-haired 19-year-old debutante whose finishing-school polish and blueblood connections had landed her a job in the White House press office.

Four days into her internship, she was invited by an aide to go for a midday swim in the White House pool, where the handsome, 45-year-old president swam daily to ease chronic back pain. JFK slid into the pool and floated up to her.

“It’s Mimi, isn’t it?” he asked.

“Yes, sir,” she said.

“And you’re in the press office this summer, right?”

“Yes, sir, I am,” she replied.

Lightning had struck. Later that day, Mimi was invited by Dave Powers, the president’s “first friend” and later the longtime curator of the Kennedy Library in Boston, to an after-work party. When she arrived at the White House residence, Powers and two other young female staffers were waiting. Powers poured, and frequently refilled, her glass with daiquiris until the commander-in-chief arrived.

The president invited her for a personal tour. She got up, expecting the rest of the group to follow. They didn’t. He took her to “Mrs. Kennedy’s room.”

“I noticed he was moving closer and closer. I could feel his breath on my neck. He put his hand on my shoulder,” she recounts.

The next thing she knew, he was standing above her, looking directly into her eyes and guiding her to the edge of the bed.

“Slowly, he unbuttoned the top of my shirtdress and touched my breasts.

“Then he reached up between my legs and started to pull off my underwear.

“I finished unbuttoning my shirtdress and let it fall off my shoulders.”

Kennedy pulled down his pants but, with his shirt still on, hovered above her on the bed.

He smelled of his cologne, 4711. He paused when he noticed her resisting.

“Haven’t you done this before?” he asked.

“No,” she said.

“Are you OK?” he asked.

“Yes,” she said.

So he kept going, this time a little more gently.

“After he finished, he hitched up his pants and smiled at me” and pointed her to the bathroom.

When she was finished, he was outside in the West Sitting Hall, where their evening had begun.

“I was in shock,” she writes. “He, on the other hand, was matter-of-fact, and acted as if what had just occurred was the most natural thing in the world.”

“Would you like something to eat?” he asked. “The kitchen’s right here.”

“No, thank you, Mr. President.”

He called a car to come pick her up and take her home.

On the ride home, it “kept echoing in my head: I’m not a virgin anymore.”

The next week, she was again invited to go swimming.

“He barely acknowledged my arrival, betraying no hint of what had happened between us just a few days before. I couldn’t bring myself to look at him in the eye,” she writes.

Later, he led her into a different bedroom. “This was the beginning of our affair,” she writes.

In a moment of reflection, Alford wonders “if I could have resisted him.

“The fact that I was being desired by the most famous and powerful man in America only amplified my feelings to the point where resistance was out of the question. That’s why I didn’t say no to the president. It’s the best answer I can give.”

She would swim with the president at noon or at the end of the workday, race back to her desk and wait for a call to visit him upstairs.

“The governing factor behind these calls, of course, was the presence — or, more accurately, the absence — of Mrs. Kennedy.”

They never returned to Jackie’s bedroom but stayed in his, which was cluttered with piles of books, magazines and newspapers.

Kennedy could be playful and tried to extract naughty things that she did as a schoolgirl. “What did all you girls do locked up in that boarding school?” he would ask. Ironically, she had attended Miss Porter’s, Jacqueline’s alma mater.

Their sex was “varied and fun.” He could be seductive and playful and sometimes “acted like he had all the time in the world. Other times, he was in no mood to linger.”

They spent an “inordinate amount of time taking baths.” Kennedy changed his shirt six times a day because he hated feeling “sweaty or grimy.”

They lined the bathtub with rubber ducks given to him as a gag gift; they named the ducks after his family members, made up back stories for them and raced them in the tub.

He taught her how to scramble eggs.

He loved popular music, especially Tony Bennett and Frank Sinatra. They shared a love for the musical “How to Succeed in Business Without Really Trying” and would sing along to it together.

Sometimes, she would spend the night with him, and he would outfit her with his own soft-blue cotton nightshirts.

But there was also distance. “There was always a layer of reserve between us, which may explain why we never kissed,” she writes. “The wide gulf between us — the age, the power, the experience — guaranteed that our affair wouldn’t evolve into anything more serious.”

She never once ran into Jackie during these flings and admits to not feeling guilty.

He sometimes invited her aboard the Sequoia, the presidential yacht, for a Potomac cruise.

On a trip to Yosemite National Park, she noticed a pattern, which she called “the Waiting Game.” She was told to stay put in her hotel until the president called for her, which meant sitting around for hours. Often, he would only call her at night

On one excursion, she met Vice President Lyndon Johnson. When she told the president about the introduction, he lost his composure.

“Stay away from him,” he commanded, likely worried that Johnson could use knowledge of the affair against him.

At the end of the summer, she told the president that she had to return to college, at Wheaton, an all-girls school in Massachusetts.

He promised that he would call under the pseudonym “Michael Carter.” And then he played a recording of Nat King Cole’s “Autumn Leaves.” He made her concentrate on the lyrics, “But I miss you most of all, my darling, when autumn leaves start to fall.”

As a parting gift, she gave him a copy of the record and trimmed the cover with leaves she had collected.

“You’re trying to make me cry,” he told her.

“I’m not trying to make you cry, Mr. President,” she said. “I’m trying to make sure you remember me.”

Within a week of her return to college, she got a call from Michael Carter.

He asked her dozens of questions: What courses was she taking? Did she like the teachers? Were the girls interesting? What did she have for dinner? He then invited her to Washington when Jackie was away.

A car service would pick her up and drive her to the airport, where a paid ticket to DC would be waiting for her.

Upon arrival, a chauffeur holding up a sign for Michael Carter would take her to the White House.

On one visit, Kennedy was embroiled in one of the most defining moments of his presidency, the Cuban Missile Crisis. For 13 days in October 1962, the United States and the Soviets were at a nuclear standoff.

Although historians have dissected Kennedy’s actions, none was privy to what he confided to Mimi.

“I’d rather my children red than dead,” he told her.

It was a chilling insight.

When the president wasn’t keeping the world from descending into war, there was plenty of wild partying. One instance was a raucous Hollywood bash at Bing Crosby’s desert ranch.

“I was sitting next to him in the living room when a handful of yellow capsules — most likely amyl nitrate, commonly known as poppers — was offered up by one of the guests. The president asked me if I wanted to try the drug, which stimulated the heart but also purportedly enhanced sex. I said no, but he just went ahead and popped the capsule and held it under my nose.”

He didn’t try it himself.

“This was a new sensation, and it frightened me,” Mimi recalls. “I panicked and ran crying from the room.”

It wasn’t her first glimpse of Kennedy’s dark side.

“He had been guilty of an even more callous and unforgivable episode at the White House” during a noon swim. Powers had rolled up his pants to cool his feet in the water. “The president swam over and whispered in my ear. ‘Mr. Powers looks a little tense,’ he said. ‘Would you take care of it?’

“It was a dare, but I knew exactly what he meant. This was a challenge to give Dave Powers oral sex. I don’t think the president thought I’d do it, but I’m ashamed to say that I did . . . The president silently watched.”

Alford, then Mimi Beardsley, says that later the president apologized to them both.

Another time, she writes, while back at Wheaton, she thought she was pregnant and told Powers. Obviously, this could explode into scandal. Abortion was illegal in 1962. Powers put her in touch with a woman who had a contact for a doctor. In the end, it was a false alarm.

There were tender moments, too.

Kennedy, alone and grieving the death of his infant child, Patrick Bouvier Kennedy, reached out for his young confidante.

“I had never seen real grief in my relatively short life,” she writes.

While Jackie was still recovering in Cape Cod, Kennedy was back at the White House.

“He invited me upstairs, and we sat outside on the balcony in the soft summer evening air. There was a stack of condolence letters on the floor next to his chair, and he picked each one up and read it aloud to me. Some were from friends and others from strangers, but they were all heartfelt and deeply moving. Occasionally, tears rolling down his cheeks, he would write something on one of the letters, probably notes for a reply. But mostly he just read them and cried. I did, too.”

One of their last times together was at a Boston Democratic fund-raiser. Ted Kennedy, the president’s baby brother, was in the room with them.

“I could see that mischievous look come into his eye. ‘Mimi, why don’t you take care of my baby brother? He could stand a little relaxation.’

“You’ve got to be kidding me,” she replied firmly. “Absolutely not, Mr. President.”

About to be married to her college sweetheart, Tony Fahnestock, she met Kennedy for the last time at The Carlyle hotel in Manhattan on Nov. 15, 1963, just seven days before his assassination in Dallas.

“He took me in his arms for a long embrace and said, ‘I wish you were coming with me to Texas.’ And then he added, ‘I’ll call you when I get back.’ I was overcome with sudden sadness. ‘Remember, Mr. President, I’m getting married.’

“ ‘I know that,’ he said, and shrugged. ‘But I’ll call you anyway.’ ”