The 76-year-old composer is concerned that Depp, who has played with rock bands since he was 13 and based his anti-hero Jack Sparrow on Keith Richards, the Rolling Stone, may be too “rock’n’roll” to play the murderous barber of Fleet Street.

Tim Burton, the London-based director behind the proposed film, has been praising Depp’s singing voice, but Sondheim needs to be convinced. The composer has said that he will not approve a cinematic version of his Broadway musical, which he describes as “virtually an opera”, if the main character has to mime rather than sing.

“He wants to make sure that all versions of his works are the best possible,” said his spokesman.

Hollywood producers acting as mediators between the New York composer and the London-based director have tracked down rock records made by Depp during the 1980s. However, on most of them Depp only plays guitar, so some other form of voice test may prove necessary.

This musical demand did not affect the previous portrayals of the Victorian era’s favourite villain. He has been played by the aptly-named but tone deaf Tod Slaughter in 1936, followed more recently by Ben Kingsley and Ray Winstone in British television adaptations.

In the original story from 1847, based on a court report in The Times, Todd cuts his clients’ throats and tumbles them into a cellar where an accomplice turns them into meat pies. But Burton wants to film the Sondheim version in which the barber is seeking revenge on a judge who destroyed his family.

Depp, 43, a half-Irish, half-Cherokee American, once described how he used rock music to escape depression and self-mutilation in his adolescence. Like other actors such as Keanu Reeves and Bruce Willis, he has carried on playing his music off-screen, appearing on Top of the Pops in 1994 with the Irish band the Pogues. He imitated Elvis Presley in his early film Cry Baby where he proved that he could sing, albeit in a stylised fashion.

A business source close to Depp said that the actor had been bemused by Sondheim’s request: “He finds it funny that there are questions about his voice as he has been singing all his life.”

Actors are not always great singers, as Clint Eastwood proved when he talked to the trees in Paint Your Wagon.

In the 1960s Marni Nixon, the soprano, secretly lent her voice to Audrey Hepburn in My Fair Lady, to Natalie Wood in West Side Story and to Deborah Kerr in The King and I.

Recently a number of actors have successfully played well known singers: Jamie Foxx won an Oscar for his portrayal of Ray Charles, followed last year by Reese Witherspoon as June Carter Cash; Joaquin Phoenix was nominated for his role of Johnny Cash in Walk the Line. Their success has encouraged studios to take more chances with raw voices.

Both Julia Roberts and Nicole Kidman have talked about signing up for a musical. A spokesman for Kidman said last week: “Of course she can sing, but how good is she? I do not know, I have not been in a shower with her.”

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