The on-off boyfriend of supermodel Kate Moss has recorded the track exclusively for the television documentary. The film will look at the complex life of Hancock, who committed suicide 37 years ago.
Doherty's adoration of Hancock is well known amongst his fans. The new track is entitled 'Lady Don't Fall Backwards' and relates to the book Hancock was reading in an episode of Hancock's Half Hour called The Missing Page.
The title of The Libertine's debut album 'Up the Bracket' also refers to a favourite Hancock phrase, "Punch up the bracket" -- a punch in the face.
Asked when he became hooked on Hancock, Doherty said: "When I was very young I think -- just as soon as I was old enough to rummage through drawers and pull out tapes -- The Unexploded Bomb, The Americans Hit Town, Sid's Mystery Tour and The Poetry Society."
The song includes the lyrics: "When nightmares come, I will sing you a song, And I will love you forever or at least until the morning comes, No don't you fall backwards, Come on and fall into my arms."
When Doherty, arrested for drugs numerous times, was given a suspended sentence in 2004 for possession of a flick-knife, he responded with a Hancock joke to questions from fans about how he was not guilty: "Innocent. What about Magna Carta? Did she die in vain?"
The film will include interviews with some of Hancock's closest friends and colleagues including co-stars Hugh Lloyd, Sylvia Syms and June Whitfield, and sitcom writers Ray Galton and Alan Simpson, who challenge some of the best-known myths about Hancock's unpredictable behaviour.
The soundtrack to the documentary also features exclusive music from The Bees.
Doherty first found fame with his band The Libertines, but it has been his publicised battle with drugs and stormy relationship with Moss, who was also in the headlines for cocaine allegations in a Daily Mirror scoop in the summer, that has made him famous.
Doherty has just released his first Babyshambles album 'Down in Albion' to mixed reviews.
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