SINCE Marilyn Monroe's untimely death, at only 36, in 1962, the Hollywood star has been the subject of many biographies and documentaries. Her chequered life-story has been told in TV movies, which delight in treating her as a macabre Cinderella figure - the waif-like would-be actress Norma Jeane Baker who, from being a Playboy centre-spread, blossomed as a major star only for her life and career to unravel in a tragic way.

Newer actresses, from Lindsay Lohan to Nicole Kidman, have done photo-shoots recreating famous Monroe roles and poses. She remains a source of fascination both to the public at large and to intellectuals and artists, who have sometimes waxed very pretentious about her. Norman Mailer, Joyce Carol Oates, her one-time husband Arthur Miller, Terry Johnson, JG Ballard and Andy Warhol are just some of the major cultural figures who have drawn on her life and persona in their work. However, very surprisingly, no major Hollywood film has yet been made about her.

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"I suppose there is always a danger that people think [playing Monroe] is impersonation and there's not a huge amount to say," suggests David Parfitt, producer of My Week With Marilyn, a new film about Monroe. The film is based on two books by Colin Clark, son of Sir Kenneth (of Civilisation fame) and brother of Alan (of the Diaries notoriety), reflecting on his experiences as a young trainee assistant on The Prince and the Showgirl. The Eton and Oxford-educated Clark struck up an unlikely rapport with Monroe, escorting her round late 1950s England and even sharing a bed with her (albeit not having sex.)

Michelle Williams, who plays Monroe, is already being talked up as a front-runner for an Oscar nomination (something which Monroe never achieved.) Parfitt remembers that Williams was initially reluctant to take on the role. "I think she tried very hard to turn it down but, in the end, the script got her." Williams's performance received glowing reviews when the film premiered at New York Film Festival last month.

"Sexy, vulnerable, fragile, alluring, seductive, delectable, complex, and all things in between, she nails it," rhapsodised veteran critic and awards pundit Pete Hammond on website Deadline Hollywood. "Williams is a sure bet for Academy recognition," agreed Screen International's Howard Feinstein.

Long a favourite of US indie cinema, Williams is arguably better known to the wider cinema-going audience for her relationship with the late Heath Ledger than for the films she has made thus far. Her searing turn opposite Ryan Gosling as the young wife dealing with a crumbling marriage in Blue Valentine (2010) showed her capacity for bringing emotional depth to her performances. Internet gossip (denied by Parfitt) suggested that Scarlett Johansson had been in line to play the lead in My Week With Marilyn. However, Williams looks to have been astute casting. She is a character actor as much as she is a star: someone bound to explore Monroe's motivations and feelings and not to rely on mannerism or to try to trade too heavily on the star's glamour.

You can see, too, why a film like My Week With Marilyn might work when a full-blown biopic wouldn't. The film focuses on a very specific moment in Monroe's career. As accounts of the making of The Prince and the Showgirl have made clear, this was a famously troubled production. Its director and star Laurence Olivier (played by Kenneth Branagh) didn't hit it off at all with Monroe.

Arthur Miller, also with her during shooting, wrote in his autobiography Timebends of the "menace" Marilyn saw in Olivier: "Finally she came to believe he was trying to compete with her like another woman, a coquette drawing the audience's sexual attention away from herself." Neither Olivier nor Miller cared much for Paula Strasberg, Monroe's acting coach and Method guru. Miller accused her of weighing down Monroe, a "natural comedienne", with "half-digested, spitballed imagery and pseudo-Stanislavskian parallelisms that left her unable to free her own native joyousness". Olivier's antagonism toward his co-star was heightened, David Parfitt speculates, by his sense that she was out-performing him. "[The Prince and the Showgirl] is not Olivier at his best. It is very stagey, very staid and she is the one who shines out. Basically, she knocks him off the screen. There is no doubt the star power is there. She knew how to act for the camera."

Along with the poisonous psycho-drama being played out behind the scenes, there was comedy too in Monroe's presence in Britain. The glamorous and voluptuous star was an incongruous figure in stuffy, class-obsessed 1950s England. The reaction she elicited from the Brits anticipated Beatlemania a few years later. "Such was the frenzied lusting to get near her - the all-American dream girl, the celluloid embodiment of erotic fantasy - that she had to be wrapped in a cocoon of protection like a head of state, and her rented home at Egham was more like a military fortress," cinematographer Jack Cardiff later recalled.

You can understand Williams's initial qualms. Portraying the film world's biggest sex symbol is a stretch, even for major stars. They must fear that they will come up just a little bit short. (It was noticeable last year how quickly Angelina Jolie sought to scotch the rumours that she had been cast as Monroe in a film.) Moreover, any truthful biopic would be a chronicle of dysfunction, disappointment and broken relationships as much as of glamour and achievement.

Some actresses who've either played Monroe or drawn on her inspiration have achieved magical results. Jessica Chastain's glamorous but very naive housewife in early 1960s Mississippi in The Help is based directly on Monroe. It's a brilliant performance precisely because it goes beyond the clichE of wiggling the hips and speaking in a cooing voice. Equally striking is Theresa Russell in Nic Roeg's Insignificance, adapted from Terry Johnson's play, which throws together versions of Monroe, senator Joe McCarthy, baseball player Joe DiMaggio and scientist Albert Einstein in the same hotel.

In contrast to such work are the tawdry made -for-TV biopics, for example Marilyn: The Untold Story, in which Catherine Hicks plays her as a slightly more emotional version of one of Charlie's Angels, or gossipy, speculative dramas like Marilyn & Bobby: Her Final Affair, exploring her alleged relationship with Bobby Kennedy. In Timebends, reflecting on his own play After the Fall (which many people saw as a veiled account of his marriage to Monroe) Arthur Miller hints at why the actress has proved such a difficult figure for film-makers to portray in anything other than the most superficial light. There was a huge gulf between her public persona and her private life: "In life, as far as the public was concerned, Marilyn was practically barred from any conceivable connection with suffering; she was the 'golden girl', the forever-young goddess of sexuality, beyond pain and anxiety, a mythically anaesthetised creature outside the reach of ordinary mortality, and hence of real sympathy." To make a truthful film would be to risk betraying the image she had worked so hard to create - and audiences still prefer to think of her as she was on screen.

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