Rolling Stones bassist Bill Wyman, model Kate Moss and Sarah Ferguson, the ex-wife of Prince Andrew, were among the mourners gathered to pay tribute to Geldof, whose coffin arrived painted with blue sky, clouds, flowers, and a portrait of her family.
Geldof, a media and fashion personality in her own right and mother of two boys aged 23 months and 11 months, was found dead at her home in Wrotham, Kent, in southern England, on April 7.
British police are treating her sudden death as "non-suspicious but unexplained". The cause remains unknown after a post-mortem examination proved inconclusive pending toxicology tests that could take several weeks.
Her father was expected to deliver the eulogy at the private funeral held at the same church in Davington, Kent, where Peaches married musician Thomas Cohen in 2012 and near where she grew up.
This was the same church where a funeral service was held in 2000 for her mother, television presenter Paula Yates, who died from a heroin overdose at the age of 41.
Peaches was the second of three daughters for Yates and Geldof, the Irish singer who rose to fame as leader of the Boomtown Rats, and later organised the charity Band Aid and Live Aid concerts to raise money for famine relief in Ethiopia.
Yates was married to Geldof from 1986 to 1996 but left him for Australian rock star Michael Hutchence, who committed suicide in 1997.
Bob Geldof said the loss of Peaches had left him and his family "beyond pain".
Making an early debut in the London glamour and society scene, Peaches wrote articles for British national newspapers from the age of 14 and was a regular on London's party scene.
But after becoming a mother, she quit the city for country life. At the time of her death, she was a columnist for Mother & Baby magazine, writing that "being a mum is the best thing in my life" and she was "happier than ever".
However she also wrote that motherhood had initially left her "friendless" and "alienated and abandoned".
Peaches' last Twitter post, the day before her death, was a photograph of herself and her mother.