There is a photograph of Marilyn Monroe, taken in 1955, in which she is reading a copy of James Joyce's Ulysses, and she is seemingly quite absorbed in the book and unaware of the camera. She still looks like a sexpot and her only visible clothing is a black and white bikini top, but she isn't turning it on for the camera – and she doesn't even appear to be knowingly turning it off, either. She looks natural, relaxed and unselfconscious.
The photograph was taken by Eve Arnold, who photographed Monroe over a period of 10 years, until the actress's death in 1962. They met when they were both young women, just starting their careers, when Monroe was a gauche and naive starlet – not the superstar she would later become. Arnold herself was a neophyte photographer, still unproven in a world dominated by men.
More than photographer and subject, the two became friends and built up a level of trust that gave Monroe the confidence to reveal herself to the camera. And more: on one occasion, during an interview, Monroe began to brush her pubic hair.
Arnold's ability to get close to people, to capture their character in those chance moments, really defined her as a photographer. She was the first female member to join Magnum in New York in 1951, which put her alongside the greats of that era: Robert Capa and Henri Cartier-Bresson. During her career, she photographed Hollywood stars and Joe McCarthy, Francis Bacon and Isabella Rossellini. She went to Inner Mongolia and photographed political prisoners in Soviet Russia. She turned on Andy Warhol's camera for him as he filmed his first feature, Harlot, although she admitted to being turned off by his attitude and his desperation to become a star.
She was almost entirely self-taught, other than a six-week photography course in New York, during which the instructor said to her: "You do not need class assignments." She learnt by experience, setting herself assignments in Harlem where she photographed fashion shows at a time when white people didn't often go there. And particularly not tiny young women like Arnold, who was only 4ft 10in tall.
The photographer Elliott Erwitt knew her during these early years. "I suspect it was harder for her but I never considered her a female photographer. She had a way of getting on with people, the mighty and the modest, in a way that was quite extraordinary. Photographers often keep a distance [from their subjects] but she didn't. She became part of the lives of many of the people she photographed.
"Maybe her size had something to do with the way she worked with people. She was a tiny, unaggressive kind of person who you wanted to pick up and be nice to," Erwitt says. "Although that was the surface. She had steel and integrity and a work ethic."
Arnold was able to deal with and photograph some of the trickiest stars of post-war Hollywood: Joan Crawford, Monroe and Marlene Dietrich. She was the first photographer to snap movie stars and movie sets as reportage, as the portrait in action, rather than the usual set up studio shots, which masked the personalities of the stars. She captured those moments when a face is unguarded and character revealed. Being one of the few female photographers could be an advantage. She was able to be part of the intimacy of the dressing room and beauty regimes with none of the awkwardness of a male photographer. And actresses seemed unusually willing to bare themselves to her.
When she photographed Crawford for the first time, the actress arrived with her two adored miniature poodles. As she passed the dogs to her secretary, she kissed each dog on the mouth and then kissed Arnold full on the mouth. She stripped off all her clothes and insisted that Arnold photograph her naked. Aware that Crawford had been drinking, Arnold reluctantly took the photographs knowing that Crawford, who was now over 50, would not be happy with the images of her body. Later, Arnold discreetly returned the negatives to Crawford and they were never seen.
With Arnold, her lens might be insightful and revealing but she was never cruel to her subjects – even if they were cruel to one another. Crawford, perhaps jealous of Monroe's youth and celebrity, described her thus to Arnold: "She didn't wear a girdle – her ass was hanging out. She is a disgrace to the industry."
Arnold made her name photographing stars, but became frustrated with the female angle and yearned for more serious political subjects. She persuaded Capa to let her photograph Senator McCarthy. It was 1954, during his time on the House Committee of Un-American activities. She described him as repellent and said that she attempted to capture the ugliness of the whole process in the faces of McCarthy and his henchmen. It was not an easy shoot, which is reflected in these pictures: they seem to lack the insight of her Hollywood work, although they are historically interesting.
One of the people that Arnold never did attempt to charm was George Lincoln Rockwell, who was head of the American Nazi Party in 1961. As she raised her camera to photograph him, he hissed at her: "I'll make a bar of soap out of you." She hissed back at him: "As long as it's not a lampshade."
She did not put her camera down and continued to photograph him at the National Convention of Black Muslims in Washington. He appears cold, sharp and uptight, with legs crossed and arms folded defensively across his chest. The darkness of his character is made plain by the large swastika band wrapped around his bicep.
Rockwell was listening to a speech by Malcolm X – the Nazis and Black Muslims had formed an alliance – and this was the real reason Arnold was there. She had been following Malcolm X for a year and had managed to charm him to the extent that he took her out to dinner in Harlem. Her photographs of Malcolm X continue to define his image – they are part of his legacy. Thirty years later, a young black photographer approached Arnold and said: "Thank you for making him look like a dude."
Arnold is now in her nineties and still lives in London, which has been her home for the past 40 years. She has had an extraordinary life, a woman born into poverty in Philadelphia in 1913, one of nine children, the offspring of Russian immigrants. Like in the movies, photography was a way out, an escape from the grind, and she hit it at a good time, just as reportage photography was entering its heyday.
"We were doing things that were more interesting than things being done today," says Erwitt. "We did big essays and we went to countries for a long time. They were golden times." And it was perhaps time that made all the difference. Arnold was able to spend time with her subjects and photograph them over years as they changed and grew up and, in Monroe's case, as they began to fall apart.
As Arnold wrote in a memoir, In Retrospect: "If the photographer has forged a relationship which permits an atmosphere in which the subject feels relaxed and safe, there is an intimacy that allows the person being photographed to be uninhibited and to reveal unknown aspects of herself."
Portraits by Eve Arnold at Magnum London Print Room, 63 Gee Street, London EC1 (020-7490 1771), 18 September to 31 November. Prints from £1,200