AS Neill, the headmaster and founder of Summerhill, the "free" school in Suffolk where lessons are voluntary and children invent their own laws, is described in A Conversation about Happiness as "a kindly grandfather figure … from another century". However, the composite portrait of him in Mikey Cuddihy's ambivalent account of her 1960s childhood at Summerhill is not particularly flattering. The towering, corduroy-clad Scot was then in his 80s: "With ears as big as a baby elephant's and hairs sprouting all over the place, his big veiny nose and his wrinkled, turkey neck, Neill is the only old man I know. The pipe, the accent, his huge feet in shiny lace-ups: he might as well be an alien from another planet." An anti-authoritarian and advocate of sexual freedom, Neill insisted staff and pupils swam naked in the school's outdoor pool: "There is something ugly, wasted and obscene about Neill's red genitalia, flapping about," she writes.

Cuddihy was raised in New York and orphaned at the age of nine when her mother, a sometime alcoholic, was killed in a car crash (she may or may not have been drunk at the time). Her father had died the same way four years earlier. He was a scion of a wealthy Irish-Catholic family, the son of a publishing magnate and cousin of the Fords and Vanderbilts. Mikey and her siblings went to live with his brother, a former investment banker, who, after a messy divorce, had returned to university to study psychology. It was he who decided to send them, in the summer of 1962, to board at Summerhill. Neill's "self-constructed, child-centred universe" in Suffolk was, according to its creator, "possibly the happiest school in the world". The exiled Cuddihys seldom saw their American family, who they presumed were engaged in a vicious custody battle over them, and were encouraged to think of Neill as a foster parent.

Neill founded Summerhill in 1921 with only a handful of pupils. An analysand and devotee of the radical psychoanalyst and sexologist Wilhelm Reich, he hoped to raise children there free of sexual repression, which he believed was the destructive force in society. "We set out to make a school in which we would allow children freedom to be themselves," Neill wrote. "In order to do this we had to renounce all discipline, all direction, all suggestion, all moral training, all religious instruction." His book, Summerhill: A Radical Approach to Child Rearing, captured the mood of the counterculture and sold 2m copies in America during the 60s (the following decade, a German translation sold more than 1m). Though the publisher excised all references to Reich, who was considered too controversial a figure for an American audience, the book followed Reich's lessons on freedom and love. "Sex with love is the greatest pleasure in the world," Neill wrote, "and it is repressed because it is the greatest pleasure."

As a consequence of Neill's late-found fame in the States, American pupils at Summerhill outnumbered English kids by two to one. Most were from California, and arrived with suntans and white-blond hair. Cuddihy was greeted by an existing student with the question: "Do you know how to play fuck-chase?" The large Victorian building had been an army HQ during the war and the boarders slept in old army bunks, almost as if they were evacuees; dilapidated Nissen huts in the grounds served as makeshift classrooms. The youngest students, referred to as Tinies, were only four or five, "all permanently shod in wellingtons with trousers tucked in, and ragged jumpers, snotty and frayed at the cuffs, and anoraks that they wear indoors as well as out". During the weekly meetings, in which the entire school met to ratify rules and distribute fines and other punishments, they clung to the teachers "like love-starved apes".

Tourists flocked to Summerhill in busloads to view the 60 students in all their feral glory. "Smiling couples stroll the grounds, arm in arm, as if they are visiting Monet's Garden at Giverny," Cuddihy writes. "They find the school surprisingly drab. We are not the flower children they were expecting to find. We are scruffy little tykes, running around the place, climbing trees, swearing and wrestling each other to the ground." Cuddihy's grandmother, having sailed over from Park Avenue on the QE2, came to visit in a Rolls-Royce with liveried chauffeur, wearing a mink coat and doused in Chanel No 5. There were occasional celebrity visitors. Joan Baez arrived, after an argument with her boyfriend Bob Dylan, and taught Cuddihy some chords on the guitar. (With the proceeds of a London concert, she helped build Summerhill's outdoor pool.) Leonard Cohen also visited, before sending his stepson to the school.

In protest at being exhibits in some prelapsarian zoo, the kids voted to ban visitors from their Saturday meetings. Neill, who was keen to show off Summerhill's democratic workings, stormed out in anger. Cuddihy writes that this was "the first and only time" she saw him blow his fuse. On other occasions the pupils exercised their right to scrap all laws and a period of riotous anarchy would ensue. Cuddihy describes a Lord of the Flies-like scenario in which a group of boys decided to start a dictatorship in an attempt to restore order. There was then a revolution to depose them, followed in turn by a fascist coup. It was a visceral lesson in politics. They enjoyed "freedom but not licence", Neill reminded them of the responsibilities of self-government, and "could do anything as long as it didn't bother anyone else".

Neill, who regretted having used the lash in his early years teaching in Scotland, was the kind of man who would join a student in throwing stones at a greenhouse so as to undermine the subversive gesture. He was not, however, the most patient of teachers: "Ach away with ye lassie; I've nae time fare the likes of you, you're wasting your time, and mine," he said, throwing Cuddihy out of his maths class. "Go and find something more interesting to occupy yerself with!" He also gave "private lessons", during which he practised wild psychoanalysis on students; in Cuddihy's case these sessions focused on her Catholicism and his suspicions of her feelings of guilt about sex. She felt her peers were "too like siblings to contemplate romance". It was common for students to get married in mock weddings, and they were allowed to sleep together. Neill's wife would take older girls to Harley Street to be fitted with Dutch caps.

More worryingly, sexual relations between students and teachers were also common. Neill's 16-year-old daughter Zoë, who has run the school since 1985, was a contemporary of Cuddihy's and is described walking around "arm in arm" with her boyfriend, the French teacher. Neill's 35-year-old stepson Myles, who taught pottery in "the best-equipped classroom in the school", had a bedroom opposite the girls' dormitory where female students liked to listen to records and smoke. According to Cuddihy, he went out with some of the more senior pupils. "Myles can get away with it, he has a special dispensation," Cuddihy writes. Another teacher was forced to leave after drunkenly groping some older girls. Summerhill was and remains essentially a family business. Because of the isolation and poor pay, she notes, "the young, sparky teachers never stay".

Cuddihy's evocative memoir is written with a deliberate naivety, similar to that of the child narrator in Esther Freud's Hideous Kinky, but it seems odd that the tone doesn't seem to change significantly in the last third of her book, which describes what happened to her after she left Summerhill. Like many former students, she was drawn to the creative professions, and is now an artist and lecturer at the University of Brighton. (She also went on an unsuccessful date with Gordon Brown.) Having swallowed Neill's rhetoric of a happy childhood, later revelations make her question how his philosophy played out in practice, and her uncle's real reasons for sending her there. "You'll be entering a world where people are repressed, emotionally crippled, and taught to hate," Neill warned school leavers. "Tread carefully."

• Christopher Turner's book about Wilhelm Reich, Adventures in the Orgasmatron, is out from Fourth Estate.