Peaches was only a girl of 11 when her mother Paula Yates died of a drug overdose in 2000 and those who knew her said it hit her extremely hard.
The last tweet Peaches sent on Twitter came on Sunday, when she posted a photograph of herself as a toddler with her mother and the caption: "Me and my mum."
Her father and family issued an anguished statement Monday about her death.
"Peaches has died. We are beyond pain. She was the wildest, funniest, cleverest, wittiest and the most bonkers of all of us," Geldof said. "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."
The statement was signed by Bob, Jeanne (his partner), Peaches' sisters Fifi and Pixie and her half-sister Tiger Geldof.
Kent police declined to name Geldof, but when asked about her death they said in a statement that officers were called to a house near Wrotham following a report of concern for a woman's welfare Monday afternoon. They said the 25-year-old woman was pronounced dead by emergency officers and that the death was being treated as "unexplained and sudden."
In an interview with the Guardian in 2009, Peaches acknowledged that she used drugs before but said she had stopped.
"'Yeah, I've taken drugs. Yes, I have had experiences, and a few of those experiences were unsavory, not ones I want to repeat, but I was growing up. I wanted the experience," she told the paper.
"I wasn't hugely into drugs, and I'm sober now," she added. "I'm not Amy Winehouse. I never have been. I wasn't a crackhead."
Peaches was married twice and leaves behind two sons, 23-month-old Astala and Phaedra, 11 months.
Her first marriage, at age 19 to Max Drummey, a vocalist with U.S. indie rock band Chester French, began at a drive-through chapel in Las Vegas. It lasted six months and ended in 2009.
Her second marriage was to Tom Cohen, lead singer of the defunct London punk band S.C.U.M
"My beloved wife Peaches was adored by myself and her two sons Astala and Phaedra, and I shall bring them up with their mother in their hearts every day. We shall love her forever," Cohen said in a statement.
Reaction across Britain was disbelief.
"It's very, very sad. Peaches has overcome a lot in her childhood, seemed to be getting her life together. You hear something like this and words can fail you. It's just tragic, terrible news," Ray Levine, Peaches' former publicist, told Sky News.