Peaches' coffin arrived at Bob Geldof's estate adjacent to the church at 12.50pm. The handpainted sky-blue coffin was covered with clouds and had a portrait of Peaches with her husband Tom Cohen, their two sons Astala and Phaedra and their pet dogs.
Locals had tied bunches of bluebells and wild flowers to the gate of Bob's Davington Priory home and the words 'RIP Peaches' were scrawled in chalk across a pillar outside the residence.
At around 2.40pm the hearse which had brought Peaches' remains to the funeral left the estate without the coffin.
Shortly after 3pm mourners started to leave the estate, some carrying the order of service with a portrait of Peaches on the front and another picture of her family on the back.
The Duchess of York was driven off in a chauffeured green Bentley and waved to onlookers as she left.
Kate Moss and her husband Jamie Hince left together after they were picked up in a black Mercedes. They were followed shortly afterwards by Jo Wood.
Other mourners included singer Eliza Doolittle, presenter Alexa Chung, music mogul Alan McGee and Bob Geldof's Boomtown Rats bandmate Pete Briquette.
Guests made their way to the picturesque church via a private gateway from Geldof's home to avoid the glare of the media.
A wreath of bright yellow sun flowers and pink lilies were delivered to the family home prior to the service.
Peaches died unexpectedly on April 7. Her husband Tom Cohen, singer with defunct punk band S.C.U.M, raised the alarm when he became increasingly concerned that his wife was not answering her phone.
Kent Police reportedly arrived on the scene to find the columnist dead with her 11-month-old son Phaedra Bloom Forever by her side.
Her death is being treated as "non-suspicious but unexplained and sudden”.
Bob was thought to lead tributes to his daughter today at the same church where the funeral of her mother Paula Yates was held.
Peaches' ashes were expected to be scattered in the estate's garden, where she played as a child, according to reports.
After the funeral, family members were expected to return to Bob Geldof’s home for a traditional Irish wake.
The funeral of television presenter Yates was held at the same church after she died from an accidental heroin overdose in 2000, aged 41.
The Geldof family has said the service was held in private.
Kent Police said the tragedy was being treated as a "non-suspicious, unexplained sudden death".
An inquest is not expected to be opened and adjourned by the coroner until after the results of toxicology tests are known.
In a statement released after her death, Bob Geldof said the family were “beyond pain”.
“She was the wildest, funniest, cleverest, wittiest and the most bonkers of all of us,” he wrote.
"Writing 'was' destroys me afresh. What a beautiful child. How is this possible that we will not see her again? How is that bearable? We loved her and will cherish her forever. How sad that sentence is.”