Sir John appeared on BBC One's Andrew Marr Show in 2008
Sir John Dankworth, a mainstay of the British jazz scene for over 60 years, has died.
Saxophonist Sir John, 82, served as musical director to the likes of Nat King Cole and Ella Fitzgerald.
Sir John, known as Johnny, died in a London hospital on Saturday. He had been ill for several months.
His wife, the singer Dame Cleo Laine, announced his death at a concert at their Buckinghamshire theatre, where she was performing with their children.
The concert on Saturday was celebrating 40 years of the theatre, which the couple founded in the grounds of their home in Wavendon.
Dame Cleo broke the news to the artists before the concert began but did not tell the 400-strong audience until the finale.
The theatre's chief executive said the family had shown "incredible" bravery.
"I think the audience had a great sense of shock," said Monica Ferguson. "There were a lot of gasps and people I spoke to afterwards were visibly shaken and moved by it."
The concert featured performances from Dame Cleo and the couple's jazz musician children Alec and Jacqui.
Celebrities such as Paul O'Grady, Prunella Scales, Maureen Lipman, Timothy West and Victoria Wood also performed.
Sir John died at the King Edward VII Hospital in central London.
In a statement, his agent said: "The all-star concert, featuring numerous British stars of stage, screen and recordings, became a tribute to John."
He was hailed by Jazzwise magazine as "one of the totemic figures of British jazz" and the UK's "first major jazz musician".
His agent Jim Murtha, speaking from New York, told the BBC it was "a sad day".
Mr Murtha added: "For British jazz and jazz around the world, I believe John has become such an international figure, particularly since he became Sir John Dankworth a few years ago."
On his Twitter page, jazz singer Jamie Cullum hailed Sir John as a "genius".
He wrote: "Sir John Dankworth, a great man and one of our finest musicians and composers, has died. Rest in peace sir."
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John Dankworth was, and always will be a legend. There will never be another like him.
Sir John and Dame Cleo met in 1950 while he was auditioning for singers with his band, the Dankworth Seven.
In 1993 Sir John formed the Dankworth Generation Band, with his son Alec.
After winning a place at the Royal Academy of Music aged 17, and following a short spell in the Army, the young Sir John was voted British Musician of the Year in 1949.
The same year he attended the Paris Jazz Festival, where he played with the legendary Charlie Parker.
In the 1960s, Sir John scored such films as Saturday Night and Sunday Morning, The Servant and Modesty Blaise and wrote the theme tunes for The Avengers and Tomorrow's World.
Sir John and Dame Cleo founded their charity, the Wavendon Allmusic Plan, in 1969, which led to the establishment of the Stables.
He was appointed CBE in 1974 and founded the London Symphony Orchestra Summer Pops in 1985.
Sir John was a fellow of the Royal Academy of Music and received the Freedom of the City of London in 1994.
He was knighted in 2006 for services to music.
In October last year he fell ill at the end of a US tour with his wife.
The couple cancelled a number of UK concert dates for the following month, although Sir John did return to the concert stage at the London Jazz Festival, playing his saxophone from his wheelchair at the Royal Festival Hall.