Virtually the first thing the visitor to Their Mortal Remains sees is a quote from the late John Peel regarding Pink Floyd’s legendary anonymity: “They could have joined the audience at one of their own gigs without being recognised.” On the face of it, that should preclude Pink Floyd as a band on which to base a V&A exhibition in the blockbusting vein of 2013’s David Bowie Is, 250m albums sold or not. Then again, as the exhibition makes clear, few bands in rock history have ever been as creative in their attempts to distract attention from themselves.

In truth, a certain anonymity seems to have clung to Pink Floyd from the start, even when they were fronted by Syd Barrett, a man as photogenic and pop-star pretty as he was talented: an early cover feature on the band in Town magazine doesn’t feature them on the cover at all, opting instead for a female model with the band’s psychedelic light show projected over her face. Nevertheless, they endured a brief moment of old-fashioned pop stardom in the summer of 1967, replete with appearances on Top of the Pops and in the teen magazines (“Syd is 5 foot 11 inches tall, with black hair and green eyes – the mystery man of the group and a gypsy at heart”). By all accounts – including the testimonies from bandmates and friends featured in a heartbreaking exhibition video – it was an experience that seemed to wreak almost as much havoc on Barrett’s fragile psyche as the vast quantities of LSD he consumed, hastening his decline.

Facebook Twitter Pinterest The exhibition plunges visitors into the psychedelic world of the 60s from which Pink Floyd emerged. Photograph: Stefan Wermuth/Reuters

After Barrett’s irrevocable descent into mental illness, a combination of survivors’ guilt, English reticence and bloody-mindedness forged in the aftermath of their frontman’s departure – when almost everyone, including their own managers, appeared to give Pink Floyd up as a lost cause – seemed to drive the band’s retreat from the limelight. Barrett’s replacement, guitarist and vocalist David Gilmour, had all the right ingredients for rock god status except the character: for all his brilliance as a guitarist, he seemed even more reserved than his new bandmates.

Pink Floyd never appeared on one of their own album covers again after 1969’s Ummagumma, and seem to have spent almost as much time devising ways of diverting their audience’s gaze as they did making music. A groundbreaking quadrophonic sound system built at their behest got almost equal billing on their gig posters, although Their Mortal Remains reveals that the grandly titled Azimuth Co-ordinator looked suspiciously like something knocked together in someone’s shed. At one show, a roadie was obliged to appear on stage dressed as a Tar Monster, complete with a penis fashioned from a washing-up liquid bottle that squirted black fluid over the front rows. The 1972 tour on which they debuted a nascent version of The Dark Side of the Moon was promoted in the press with a photo of the band with their backs to the camera. Come and see us live, but don’t look at us: that seemed to be the message.

Facebook Twitter Pinterest The album cover for The Dark Side of the Moon. Photograph: Courtesy of V&A

Their masterstroke came with The Dark Side of the Moon’s release the following year. Early 70s rock was filled with striking images, from Bowie’s lightning flash makeup to Led Zeppelin’s mystical Zoso symbols, but few had quite the same lasting impact as the refracting prism design that Pink Floyd’s longstanding visual team Hipgnosis came up with for that album’s cover. An entire room of the exhibition is devoted to it, and rightly so. In cynical modern parlance, it was a brilliantly simple piece of corporate branding; 44 years on, it remains the image that first springs to most people’s minds when the name Pink Floyd is mentioned – although Hipgnosis’s designs for their subsequent albums were scarcely less iconic: the photograph of two businessmen shaking hands, one in flames, for 1975’s Wish You Were Here; the shot of a giant inflatable pig floating above Battersea power station for 1977’s Animals, a giant neon replica of which fills another of the exhibition’s rooms.

Facebook Twitter Pinterest A room full of Hipgnosis artwork for Pink Floyd’s Wish You Were Here. Photograph: Daniel Leal-Olivas/AFP/Getty Images

The Dark Side of the Moon made Pink Floyd global superstars, but the bigger they got, the more Pink Floyd themselves seemed to recede. A 1974 tour programme attempts to elicit information on the band members via a questionnaire, to no avail: “Personal likes: ‘Not much.’ ‘Too personal’.” On stage, they were dwarfed first by a giant circular screen showing specially commissioned films, then by enormous inflatables and vast parachutes in the shape of sheep.

Facebook Twitter Pinterest One of Gerald Scarfe’s creations for The Wall. Photograph: Facundo Arrizabalaga/EPA

By the time of 1979’s The Wall, they were sending other musicians on stage in their place, wearing rubber life-masks based on their faces, and performing behind 40 feet of cardboard bricks onto which Gerald Scarfe cartoons were projected. Their Mortal Remains makes an intriguing attempt to link their ever-more complex stage designs with Roger Waters, drummer Nick Mason and keyboard player Richard Wright’s background as architecture students, although others at the time took what you might describe as their elaborate reticence for haughtiness and pomposity: one wall of the exhibition is devoted to their one-time labelmates the Sex Pistols, with Johnny Rotten’s I HATE PINK FLOYD T-shirt at its heart.

Facebook Twitter Pinterest Masks worn by a four-piece ‘surrogate band’ who opened The Wall live show each night. Photograph: Lauren Hurley/PA

Waters’ acrimonious mid-80s departure from the band is tactfully skirted around, although keen students of Pink Floyd’s endless icy, passive-aggressive internal struggles might note with interest the glaring disparity in space afforded Waters’ last album with the band, The Final Cut, and their first without him, 1987’s A Momentary Lapse of Reason. The latter gets a whole room, which seems less a reflection on its contents – curiously more dated-sounding now than the music they made in 1967 or 1973 – than on the vast, box office-busting tour it spawned, which tellingly saw Pink Floyd reprising not just their greatest hits, but their most famous visual effects. To the evident fury of Waters, who considered himself the band’s creative genius, it didn’t seem to matter to audiences whether he was there or not, as long as it sounded like Pink Floyd and an inflatable pig floated over the crowd: such is the downside of carefully cultivated anonymity.

Or perhaps it did matter. There’s something touching about the way Their Mortal Remains concludes not with The Endless River – the largely instrumental album Gilmour and Mason constructed in tribute to Richard Wright, who died in 2008 – but with footage of the quartet’s solitary reunion, at Live 8 in 2005. Their performance ends with a slightly uneasy group hug, which one band member has to be visibly coerced into joining: Pink Floyd were awkward in the spotlight until the last.