Squinting through narrowed eyes beneath a fedora, a cigarette hanging from his thin lips, his world-weary expression forged by hard liquor and hard-bitten women in smoke-filled bars, Humphrey Bogart was Hollywood’s iconic tough guy.

In classic movies from The Maltese Falcon to Casablanca, and The Big Sleep to The African Queen, he embodied the tough, cynical American who men wanted to emulate and women found irresistible. So when his beautiful 19-year-old co-star Lauren Bacall fell in love with the 45-year-old Bogart while filming To Have and Have Not, in 1944, they became a power couple in one of Hollywood’s most legendary marriages.

Yet it was all a facade, reveals a new biography, Bogie & Bacall.

“Bogart and Bacall were both riddled with insecurities,” says author William J Mann. “Scarred by a loveless childhood, he had a self-destructive streak that tore through three broken marriages before he found her.

“Bacall never got over being abandoned by her father when she was nine years old, struggled financially, and though she denied it to her dying day, was looking for a father figure when she found Bogie.”

It was one of Hollywood’s most fabled romances, yet tragically short-lived: Bogart died of oesophageal cancer in 1957, aged 57, when Bacall was just 32 years old. The duo had starred together in four films and produced two children.

Their screen debut together in To Have and Have Not proved to be movie magic. Forever after, they called one another by their characters’ names: Steve and Slim.

“It’s one of the rare times we saw two people fall in love on screen,” says Mann. “The chemistry between them combusted.”

In one famous scene, Bacall is leaving Bogart when she turns to say that if he needs anything he should just whistle for her.

“You know how to whistle, don’t you, Steve?” she asks seductively. “You just put your lips together and blow.”

Says Mann: “It was such a sensual scene. But Bogart struggled with his feelings for Bacall. He couldn’t deny the attraction, but didn’t want to end his volatile third marriage, and was afraid his wife, actress Mayo Methot, might take her own life.”

Yet Bogart could not resist Bacall’s husky-voiced allure.

He stole a kiss in her dressing room, sparking an affair that doomed his marriage. But it was a romantic, vulnerable and insecure Bogart – very different from his screen persona.

“Hollywood made Bogart appear cynical, ruthless, hard-bitten, anti-romantic and unsentimental,” says Mann. “But far from being a street thug, he was the son of a wealthy doctor; he never played truant or was in trouble with the police.”

Behind his street-hardened image Bogart was a very different man.

“He felt unloved and undervalued since birth,” says the author. “His parents were both addicted to morphine, and his mother was a workaholic, and they never hugged or kissed their son, or showed him any affection. He failed at school, failed at every job he tried, and grew up insecure. Bogart struggled with self-worth all his life.

“He struggled in relationships, scared of marrying a woman who might put her own career first. His first three wives – actresses Helen Menken, Mary Philips and Methot – all took second billing to him in their lives. He was sexist and misogynistic. He spent his life searching for his mother’s love: that’s what he wanted from his wives.”

Bogart was Hollywood’s highest-paid actor after his famous 1944 hit Casablanca, and with Bacall he made four classics: To Have and Have Not that same year, The Big Sleep in 1946, Dark Passage in 1947, and 1948’s Key Largo.

Bacall was born Betty Joan Perske, and was discovered by director Howard Hawks after modelling for a magazine cover. He changed her name to Lauren Bacall, which she loathed.

Bogart lovingly called her “Betty”.

“Bacall was madly in love with Bogart, the father figure she’d never had,” says Mann.

“She’d had a troubled childhood, with an abusive father who left when she was nine. Her family warned her not to marry a thrice-divorced alcoholic 25 years her senior who was drinking, smoking and coughing all the time, but she married him anyway.”

When Bacall got pregnant, Bogart was furious.

“He needed his wives to mother him,” says Mann. “He saw a baby as his rival for Bacall’s affections. And he wasn’t a good father: he starved his son, Stephen, of affection, just as he had been emotionally deprived as a child.”

Despite their passion, Bogart and Bacall were far from faithful to each other.

He had a long-running affair with his hairdresser, Verita ‘Pete’ Peterson Thompson, the woman entrusted with Bogart’s full-frontal toupée. Bacall also had her head turned, by Frank Sinatra and by the charismatic American politician Adlai Stevenson – another father figure – who unsuccessfully ran for the presidency in 1952 and 1956.

Bacall devotedly followed Stevenson across the US as he campaigned.

“From her letters and memoirs, it seems quite likely they had a sexual relationship,” says Mann. “Stevenson entranced her and awakened an intellectual side of her. Then she grew very close with Sinatra, but I don’t believe they became lovers until after Bogart died.

“But just because Bogart and Bacall both took lovers doesn’t mean that they weren’t fully in love with each other.”

Bogart did not age well alongside his young bride.

“He was never going to be a good-looking leading man alongside Clark Gable or Cary Grant, but years of alcohol and cigarettes took their toll, and at 50 he looked 65, with a persistent cough.”

He was diagnosed with oesophageal cancer but his doctor never told Bogart he was dying until he had just weeks left.

“Bacall became Bogart’s loving and loyal nursemaid, sleeping beside him in his sickbed, making sure he was comfortable,” says Mann.

“His death wasn’t unexpected, but still left Bacall devastated. Worse, she found herself abandoned by Hollywood and her friends. When Sinatra arrived to comfort her, she welcomed the romance.”

Bacall and Sinatra became lovers, and one night he proposed marriage.

“Bacall instantly leaked the news to the press, and Sinatra was horrified,” Mann adds. “He felt he was being trapped into marriage, so he abruptly ended the engagement. He treated her appallingly.”

Bacall struggled to survive in Hollywood without Bogart, turning to Broadway where she found success, yet still felt she was only valued for being Bogart’s widow.

“She lived with a sense of being an imposter, unworthy of what she’d been given,” says Mann. “She never fully believed she had earned the world’s acclaim, and was often consumed with contempt and resentment for others. She couldn’t understand why she never received an Oscar nomination, or why she was not offered the roles that went to other actresses. She felt like she was seen as half of Bogie & Bacall, and without him felt like a fraud.”

Bacall went on to marry actor Jason Robards, but never stopped loving Bogart, protecting his memory in her hagiographic memoirs.

“The real Bogart was gentler, more romantic, and yearned for affection more than the Bogart of Hollywood myth,” says the author. “With Bacall, for a few brief years, he found that love.”

Bogart’s ashes were interred at the Forest Lawn cemetery in Glendale, California.

In his funeral urn was a small gold whistle from the charm bracelet he had given Bacall before their wedding – a nod to perhaps their most famous scene.

Fifty-seven years later, Bacall’s ashes were laid to rest alongside him.

• Bogie & Bacall: The Surprising True Story of Hollywood’s Greatest Love Affair by William J Mann (HarperCollins, £35) is published on August 3. For free UK P&P, visit expressbookshop.com or call 020 3176 3832