Kate Moss, musician Jools Holland and former Rolling Stones bassist Bill Wyman were all pictured at the service.

The Duchess of York, journalist Mariella Frostrup, actress Jaime Winstone, TV presenter Alexa Chung, and Radio 1 DJ Nick Grimshaw were also there.

The Duchess of York arrived in a chauffeur driven car

Peaches' coffin was painted sky blue, with a painting of her family on the back and peaches and clouds on the side.

Sir Bob Geldof was expected to lead the tributes to his daughter, who died two weeks ago in "unexplained" circumstances.

The private service was at the same Kent church which held the funeral of Peaches' mother, Paula Yates, in 2000.

Actress Jaime Winstone is at the funeral

St Mary Magdalene and St Lawrence Church in Davington, near Faversham, is also where the 25-year-old married musician Tom Cohen, the father of her children, in 2012.

It is also where her mother - who died from an accidental heroin overdose - married Boomtown Rats singer Geldof in 1986.

Ms Geldof's ashes are expected to scattered in the garden of Sir Bob's Davington Priory estate, which is next to the church.

Mystery still surrounds the sudden death of Ms Geldof on April 7.

DJ Nick Grimshaw makes his way into church

Her body was found at the Wrotham, Kent, home she shared with her husband and their children after officers were called "following a report of concern for the welfare of a woman".

Sir Bob paid tribute to his daughter alongside his partner Jeanne Marine, and Ms Geldof's sisters Fifi Trixibelle, Pixie and Tiger, saying she was the "wildest, funniest, cleverest, wittiest and the most bonkers of all of us".

Her older sister Fifi posted a picture of the siblings together on Instagram and wrote: "My beautiful baby sister ... Gone but never forgotten. I love you, Peaches x".

Ms Geldof had two sons with Mr Cohen - Astala, 23 months and Phaedra, 11 months.

Kent Police said her death was being treated as "non-suspicious" and "unexplained".

An inquest is not expected to be opened and adjourned by the coroner until after the results of toxicology tests are known.

Peaches with her husband of two years, Tom Cohen

Ms Geldof was 11 when her mother died from an accidental heroin overdose at the age of 41.

The last tweet she posted on the day before she died was a picture of herself as a child with her mother, with the message "me and my mum".

Peaches (right) with her father and siblings in 2005

She often spoke about her struggle to cope with her parents' break-up when she was seven and admitted to experimenting with drugs during her teenage years.