With her trademark bob and shades, a basic but effective look that she has maintained since the 1960s, Anna “Nuclear” Wintour is the most feared woman in fashion. The editor of US Vogue remains most famous as the inspiration for the demanding bitch played by Meryl Streep in big-screen fashion satire The Devil Wears Prada. So you might expect Wintour to be a target rather than a subject.

Yet R. J. Cutler’s documentary film, unveiled at the Edinburgh Film Festival, does a terrific job of humanising her. It’s light on biography and Wintour’s private life is barely touched on. But, up close, she comes across as surprisingly girlish and even rather sexy with her shy smile and button nose. Rather than indulge the stereotype of the lady boss from hell, The September Issue creates a sympathetic portrait of a woman on top, driven by passion but without tact.

In theory, The September Issue ought to be just a study of the production of the autumn edition of the style bible Vogue, the telephone directory-sized issue that heralds the arrival of the winter collections.

This immediately raises expectations: of a world based on tantrums and outrageous glamour, of trousers with three legs and naked airhead models wearing shoes for hats.

Instead, Cutler’s film is less dramatic but no less engrossing. It’s clear from the outset that fashion will be accepted in all its trivial glory, but rather than focus on the decisions being made — perhaps the film’s biggest failing — it focuses on the decision-makers: ice-queen editor Wintour and creative director Grace Coddington, the unexpected heroine of the piece.

Though it never quite deals with the practicalities of the magazine world (the film really depends on whether you trust Wintour’s black-and-white judgments, which seem to amount to an airy yes or no), the film is very good on the to-and-fro-ing of the process.

In one memorable scene, Coddington is shown arguing the case for a photoshoot celebrating textiles; Wintour successfully argues for the removal of a dress that looks like a binbag, saying she’d prefer the clothes to be “more wearable than not”.

Coddington, meanwhile, is revealed as the power behind the throne. A former model, she plans and executes Vogue’s famous fashion shoots with an infectious enthusiasm that is wonderful to watch.

For non-believers, the film may not do enough to interrogate the ludicrously lucrative fashion industry, but an awareness of its silliness is there. In a scene straight out of Brüno, a designer is told that his work will feature in the pages of the legendary September issue itself. “Ooh!” he enthuses. “When’s it coming out?”

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