A pair of Friesian horses with black plumes drew a glass-sided carriage containing his coffin, draped in a black cloth.
A traditional horse and carriage led the cortege from Belsize Park, north London, picking up mourners from his family home in Hampstead and passing near Kilburn High Road, which gave its name to his first band.
A pair of Friesian horses with black plumes drew a glass-sided carriage containing his coffin, draped in a black cloth.
Members of the band Madness acted as his pall-bearers at Golders Green crematorium.
Dury, who died after a long battle with cancer aged 57, was one of their inspirations and performed on their recent single Drip Fed Fred.
Robbie Williams travelled to Sri Lanka with Dury in 1998 to work for the charity Unicef, while Mo Mowlam was a fan of the singer, who had seen him in concert weeks before he died.
Other mourners included BBC Radio 1 DJ Annie Nightingale, who championed Dury's career in the late 1970s, and musician Nick Lowe, a label-mate of his on Stiff Records.
Humanist Annette Furley, who conducted the service, said: "He was one of the few original personalities in the music business.
"He used to write music that made you want to dance and also made you laugh.
"He was aware that he couldn't sing but he knew that he had a good feeling for tempo and rhythm.
"When told a year ago he was going to die, in true Ian style his reaction was 'Oh blimey'."
"He inspired all those around him and changed people's lives. Many people have said what they did because of Ian."
"He continued to gig even through his illness and he never lost his sense of humour. Even on the day he died he was still telling jokes."
There were more than 60 wreaths for the singer, many of them tongue-in-cheek.
One was a floral tribute in the shape of a pint of Guinness, another shaped like a guitar, and one from Madness, reading "Uncle Ian from Madness".
Others read "Oi Oi", "Dad", and "Durex" - a play on his name.
His second wife, sculptor Sophy Tilson, was at the crematorium, along with their children Bill and Albert. His grown-up children, Jemima and Baxter, from his first marriage to Betty, were also there.
Many watched the service on a TV screen outside.
Dury's band, The Blockheads, performed a song on which he had worked with them in the week before his death.
After the service, Robbie Williams called him a "wonderful man".
"Because of Ian I went to Sri Lanka with Unicef. I am off to Mozambique this year to carry on Ian's work," the singer said.
"He's been an inspiration - as a person and as a musician - and my thoughts are with his family and friends. May he rest in peace."
Mourners then continued the service by heading to the Forum venue in Kentish Town, where Dury performed when it was called the Town and Country Club.