Picasso's largest work is to go on show nearly half a century after the Victoria & Albert Museum acquired it despite lacking the space to display it.

The 10m x 10m (33ft x 33ft) stage frontcloth will form the centrepiece of a major autumn exhibition exploring the world of Serge Diaghilev, the Russian impresario who made ballet one of the most dynamic artforms of the early 20th century.

Picasso became an integral member of the company during the First World War and was involved in creating the designs for nine of its ballets.

He was one of the many artistic geniuses who collaborated with Diaghilev and whose work will be on show in the exhibition. Others include Vaslav Nijinsky, Igor Stravinsky, Coco Chanel and Henri Matisse.

The ballet Le Train Blue, a lighthearted piece about the fashion world, was first staged in Paris in 1924 with costumes by Chanel, libretto by Jean Cocteau, choreography by Bronislava Nijinska, Nijinsky's sister, and the huge curtain by Picasso which greeted the audience while the overture played at the start of the evening.

Picasso's frontcloth shows two rotund women gambolling across a beach. Scene painters enlarged it from the original painting, Deux Femmes Courant, and the artist himself was so delighted with the result that he signed the bottom of the canvas and dedicated it to Diaghilev.

Its working life came to an end in 1968 when a group calling themselves the Friends of the National Museum for the Performing Arts bought it for £69,000 from a Mr Tony Diamantidi, the president of the Diaghilev and De Basil Ballets Foundation.

Their hope was that the frontcloth would become the focal point of a performing arts museum attached to the V&A.

However the organisation that they envisaged, which came into being as the Theatre Museum in Covent Garden in 1987, never had the space to show it off.

Instead the canvas's outings have been limited to gala fundraisers and a weekend apearance at a fair in Olympia in the 1970s and a press call in 2003, when it was unrolled on a floor at the Royal Opera House as part of an appeal to raise funds for the Theatre Museum.

When the museum closed in 2007 its collections were brought back under the V&A's wing.

Jane Pritchard, the curator of Diaghilev and the Golden Age of the Ballets Russes 1909-1929, said: "There is a bitter-sweet element to it but on the other hand you've got to say that things have worked out really quite well for the theatre and performance collection and the fact that it can now be shown at the V&A is an indication of that positive outcome."

A maverick with a formidable temper, a taste for very young men and an eccentric dread of the sea, Diaghilev was also a great creative talent.

A recent biography begins with the claim that he "transformed the world of dance, theatre, music and the visual arts as no one had ever done before (or has done since)".

Perhaps his most notorious work was the ballet The Rite of Spring with music by Stravinsky and radical choreography by Nijinsky. The Paris premiere in 1913 triggered a riot.

The V&A has the largest collection of Ballet Russes costumes in the world, including those designed by Matisse, Picasso and Chanel.

The exhibition will also feature set designs, props, musical scores, notes on choreography and posters.

Picasso's stage cloth will not be the largest in the show, however.

Natalia Goncharova's stage backcloth for the final scene of The Firebird (1926) is 10 metres high and 16 metres long.

The exhibition runs at the V&A in London from September 25 to January 9, 2011.