On a late spring afternoon in 1967, the 17-year-old model Twiggy, born Lesley Hornby in Neasden, northwest London, and her manager Justin de Villeneuve, actually Nigel Davies from east London, touched down at New York’s JFK airport. Within minutes they found themselves caught up in a seething mass of photographers, journalists, fans and bystanders. The sheer weight of numbers overshot a safety barrier and headed towards the landing gear. Britain’s hottest property had arrived.

Fashion, pop culture and celebrity collided to produce a new kind of woman who looked nothing like a woman usually looked. Her hair had been scissored into a blond, boyish crop; at 5ft 6in she was impossibly angular, but her expression of saucer-eyed bewilderment, emphasised by three rows of false lashes, was real enough: “I felt I was from outer space. Everyone wanted to come and look at me.”

It had taken less than a year for Twiggy, the Daily Express’s Face of ’66, to become the world’s most recognisable model. “Twiggy is called Twiggy,” Vogue explained, “because she looks as if a strong gale would snap her in two.” Handsome, imperious and very persuasive, de Villeneuve kept the engine revving. So completely was Twiggy plugged into the zeitgeist she was almost an extension of the camera. Everyone paid tribute: Richard Avedon, Bert Stern, Helmut Newton, David Bailey (they didn’t get on) and Guy Bourdin (her legs only). Presently de Villeneuve would keep a tighter hold on it all by becoming her sole photographer.

By 1967 she was also a brand with her own magazine (Twiggy), fashion line, Twiggy Stix eyeliners and lunchboxes. “The machine had started to roll,” de Villeneuve exulted. “And I was running alongside oiling the wheels.” Here she is that same year, at the height of it all in a very of-the-moment ensemble, a floral daisy print dandy suit with matching shorts – and long false eyelashes. Vogue’s photographer was the up-and-coming Frenchman Just Jaeckin, who would go on to have a career in films, most notably as director of soft-porn classics Emmanuelle (1974) and The Story of O (1975).

By 1970, Twiggy had retired from modelling – but her fame would far outlive a fad for triple-layered false lashes and a range of dolls. She turned into a star of films and musicals, most notably The Boy Friend (1971) and a bona fide Broadway smash in My One and Only (1983).

Out this month is Twiggy, a celebratory documentary on Dame Twiggy Lawson, as she is called today, directed by Sadie Frost. What fascinates Frost about Twiggy is how she is “always challenging herself but never selling out or compromising herself or her family”. Almost 60 years after her heyday, Twiggy is still “strong, dynamic, savvy, sweet, sexy and sophisticated”, says Frost. “She is a mix of androgyny, rebellion and girl next door. She encompasses everything I respect in a woman.”

Twiggy is in cinemas now