DOROTHY'S ruby slippers, Holly Golightly's Givenchy gown, Travis Bickle's combat jacket, Indiana Jones's fedora, Scarlett O'Hara's "curtains" dress, Tony Manero's Saturday Night Fever suit – it is the wardrobe of which cinema dreams are made, and now mere mortals can step inside with Hollywood Costume, a new exhibition at the V&A in London.

Five years in the making, Hollywood Costume brings together more than 130 landmark costumes from a century of filmmaking, from Chaplin's Little Tramp to the high-tech threads of Avatar. If you've ever wanted to get within a couple of feet – but no touching, please – of The Dude's dressing gown from The Big Lebowski or Tippi Hedren's tailored suit from The Birds, follow the tarmacadamed road to the V&A on a visit to London.

The exhibition was the idea of Deborah Nadoolman Landis, the Oscar-nominated costume designer on films including The Blues Brothers, Raiders of the Lost Ark, Michael Jackson's Thriller short film, and Coming to America.

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Costume design is one of the Cinderella sectors of the film industry, with its "stars" often lost in the list of end credits. Yet as the exhibition shows, their work is crucial in bringing a character to life.

"It's a very tricky thing about costume designers because our work should be invisible," says Nadoolman Landis. "We're punished for our virtuosity. We leave no fingerprints. You shouldn't notice an individual designer's personal style in any film. It's like the opposite of fashion. There are no labels in costumes."

Working with guest curators Nadoolman Landis and Sir Christopher Frayling was Keith Lodwick, assistant curator at the V&A and the set and costume designer on more than 30 stage productions. It fell to him to do a fair chunk of the detective work and trace the costumes or artefacts (some were closer than others: Steven Spielberg's original stick man drawing for how Indiana Jones might look was on the bedroom wall of Nadoolman Landis's son for 30 years).

"Hollywood studios began to sell off their material assets in the Seventies," says Lodwick. "MGM famously had a sale in 1970 where they sold the ruby slippers [from The Wizard of Oz] for $15,000. It's hard to know what they are worth today."

Hollywood doesn't really glance back, says Lodwick, preferring to look forward to the next box office hit instead. With the exception of Warner Bros, archiving costumes was not generally the done thing. That has changed recently, due to the rise of eBay and auction houses holding sales of celebrity artefacts.

"Costumes from the golden age weren't kept, they might have been kept by the actor, or they have simply been lost." Pieces are scattered around the world, he adds, in private hands, museums and archives.

As well as contacting archivists, museums, designers and directors, Lodwick found himself chasing leads. There was a rumour, for example, that Quentin Tarantino had kept Uma Thurman's yellow jump-suit from Kill Bill. It turned out to be true, and Tarantino loaned it to the exhibition.

Some costumes proved more difficult than others to secure. The curators were able to get the blue and white gingham pinafore dress worn by Dorothy/Judy Garland in The Wizard of Oz. Designed by Adrian, this is the costume's first time on display in the UK. Dorothy's ruby slippers, however, were a trickier affair. There are only two pieces in the exhibition protected by glass: the ruby slippers, and Marilyn Monroe's famous "air vent" white dress from The Seven Year Itch.

There are still a few pairs of the ruby slippers in existence. The Smithsonian in Washington DC has a pair, and they are such a popular draw the carpet around the case has to be replaced regularly. There are two more pairs in private hands, but the collectors did not want them to leave the US.

The Smithsonian strode to the rescue and said yes to a loan – but just a temporary one. The slippers have to be back in the US in time for Thanksgiving, so will only be at the V&A until November 18.

After that, the Smithsonian slippers will be replaced by a replica pair made by the original makers, Western Costume, using the 1939 pattern. Ruby slippers after November 18 aside, everything else in the exhibition is the genuine, as worn by the stars, article.

The exhibition also features exclusive interviews with Meryl Streep and Robert De Niro, talking about the importance of getting the costume right.

Streep says: "On every film, the clothes are half the battle in creating the character. I have a great deal of opinion about how my people are presented. We show a great deal by what we put on our bodies."

Many of her costumes are featured, from the skirt suit worn in the Thatcher biopic The Iron Lady, to a sparkly jump-suit number from Mamma Mia. The De Niro costumes on show include those from Raging Bull, Taxi Driver, and Casino. In Taxi Driver, those who worked on the film recall, De Niro loved the costume so much he wore it all the time.

Advance bookings for Hollywood costume have been running at record levels, suggesting the demand to see these garments, and learn about their place in film, is huge.

"People are very drawn to costume because it is the nearest you can get to that person, that character, that actor," says Lodwick.

V&A, London, until January 27, 2013.