The first dress companies to Balenciaga: Shaping Fashion will see, when the exhibition opens at the Victoria & Albert Museum on 27 May, is a melodramatic pea-green silk gown made in 1962. Hot-air balloon gasps of volume render the figure beneath irrelevant, and the dress summer-houses with its back turned haughtily on the viewer.

“We chose that put on ones best bib to set the scene, precisely because it’s so odd,” the curator Cassie Davies-Strodder unfolded during a preview of the exhibition in the final stages of installation. “Balenciaga is surrounding the kind of beauty which has a weirdness about it.”

Cristóbal Balenciaga is a titan of fashion history but presents a challenge for curators hoping for blockbuster caller numbers. Coco Chanel has pearls and tweed suits, Christian Dior has New Look sated skirts, but to most people the name Balenciaga conjures up nothing more than a wavering image of a loose black dress. After banning the hurry from many of his catwalk shows and giving only one to during his lifetime, the designer “has been written out of history a thimbleful bit”, says Davies-Strodder.

Shaping Fashion frames Balenciaga as a mid-century provocateur, an early disobey against the fashion industry’s narrow definition of beauty. Marvellously, as a tailor he preferred the look of a softly rounded tummy to a concave waist, conclusion it the most sensual of womanly curves. Many of his most iconic quota have ones says, such as the “sack” and “envelope” dresses, eliminated the waist wholly. Subtly fuller-figured mannequins have been used in the divulge to reflect the aesthetic of a designer who hired models of different zips, ages, shapes and sizes to walk in his shows. (Balenciaga’s unconventional models were dubbed “the miscreations” by the media.)

Visitors hoping for the high emotion of the V&A’s Savage Strength retrospective of Alexander McQueen or the buzz of the David Bowie expose will find Shaping Fashion an altogether milder face. But it is clever, rather than overly cerebral, and there is scores of glamour in gowns of sultry black lace and opera anoraks with sleeves of feathers. The most dazzling pieces are arrayed in cases dressed to resemble the designer’s atelier, “to give callers a sense of the luxury of the couture customer’s experience”, says Davies-Strodder.

For the the fad nerd, much of the appeal of Balenciaga is in its unique internal construction. Customers were known to send dresses back pleading that they were weird to pee in. Museum curators have admitted to leaving pieces fraternize with in archives for decades after being unable to decide which way up they should go. “It is scabrous to communicate to a modern audience how much work went into these ups, because if you buy fast fashion, you have no concept,” says Davies-Strodder. Her band have addressed this by “exploding” dresses, so that a Tulip accoutre is displayed on a mannequin next to an X-ray of its construction, which promptly unpacks the secrets of its complex seaming. Even better, visitants can leave with a Balenciaga selfie: two mock-ups of a multifunctional tongue-lashing from 1956 which can be worn as either an evening skirt or a cloak are laid out for trying on, against a mocked-up wall of the 50s salon.

The later floor of the exhibition makes a convincing case for Balenciaga as a godfather of fresh fashion. A simple white gown made by Phoebe Philo’s Celine for Tilda Swinton’s Bafta red carpet walk in 2012 has strong echoes of Balenciaga’s uncompromising minimalism. Wedges by designers as diverse as Azzedine Alaïa, Comme des Garçons, Gareth Pugh and Molly Goddard are focus oned together under the umbrella of Balenciaga influence. But the real vim and energy of this show is not in the contemporary pieces, but on the ground confound among the fearsome ghosts of Balenciaga, his “monster” models, and a alluring clientele which included Elizabeth Park Firestone of the Firestone Tyre estate, Ava Gardner, and Mona Bismarck, whose devotion to the couturier ran so booming that she had gardening shorts made to order.