He became a household name in 1960 thanks to Oliver! but spent the next 20 years addicted to drugs and alcohol.
Linked romantically to a bevy of celebrities, most notably Alma Cogan and Judy Garland, he never married and in later life came out as a homosexual.
At times, his life appeared to be a continuous party with the Beatles and the Rolling Stones among his celebrity friends.
Bart, who was being treated at the Hammersmith Hospital in London, led the revival of the British musical at a time when American productions dominated the capital's stages.
Born Lionel Beglieter, Mr Bart was the son of a Jewish tailor in London's working-class East End. Unable to read or write music, his abilities were still recognised by his teacher and he won a scholarship to St Martin's School of Art at 16.
While working as a set painter he spotted a notice asking for song writers and applied under a new name inspired by a bus journey past St Bartholemew's Hospital.
In 1959, Bart wrote "Living Doll" for Cliff Richard, which stayed at number one for six weeks. The same year his first musical, Fings Ain't Wot They Used T'Be, premiered, then followed Lock Up Your Daughters.
In 1960 came Oliver! Originally rejected by six venues, it sold 30,000 advance tickets in the first week and went on to a long run followed by successful revivals in 1967 and 1977.
It was also a New York hit, winning a Tony (Broadway's Antoinette Perry award). The film adaptation, starring Ron Moody as Fagin, won six Oscars.
Mr Bart went on to write the music and lyrics for Blitz! in 1962 and Maggie May in 1964, and then composed the music for Lionel in 1977.
But two other musicals, Twang! in 1965 and La Strada in 1969, were savaged by critics. By the late Sixties he was in constant need of drugs and alcohol and it was to be nearly 20 years before he was "clean".
In 1972, he filed a petition for bankruptcy, with estimated debts of pounds 158,000. Part of his financial problems stemmed from signing away the rights to Oliver!, which cost him as much as pounds 100 million. His problems continued with a year ban for drink-driving in 1975 and in 1983 he was banned again for two years.
By the late 1970s, he had diabetes and had moved to a flat in Acton, west London, where he lived surrounded by packing cases full of his former life.
Despite his fame, he often admitted that money meant very little to him. He once told a newspaper. "I hated money, I had no respect for it. My attitude was to spend it as I got it."
In recent years, he tried to revive Quasimodo, a musical which he had written in the early 1960s and had based on Victor Hugo's 1831 novel.
"I remember when I'd written some of the music and lyrics I sent the script to Noel Coward," Bart said in an interview with Independent on Sunday in 1995. "He said: `Brilliant, dear boy, but were you on drugs when you wrote it? It seems a little bit abstract here and there.' I suppose it was."
Funeral arrangements for the composer, who is survived by two sisters, have yet to be announced.