Geldof was pronounced dead by paramedics at her home in southeast England on Monday.
Kent Police said a post-mortem examination had not revealed the cause and a toxicology report could take several weeks.
Geldof, the daughter of Irish musician Bob Geldof and the late TV presenter Paula Yates, had worked as a model, writer and television show host.
She grew up in the glare of Britain's press, which reveled in the late-night antics of her teenage years, and in the shadow of her mother's death from a drug overdose when Peaches was 11.
More recently she had married for a second time, to musician Tom Cohen, had two young sons and worked as a broadcaster and fashion writer. She said in 2009 that her drug-taking years were behind her.
In a column for Mother and Baby magazine, published the day after her death, Geldof wrote that motherhood had made her "happier than ever."
"I've achieved a sort of perfect balance," she wrote. "Right now life is good. And being a mum is the best part of it. "
Police are treating her death as non-suspicious but unexplained. The force said detectives are investigating the circumstances and will hand their report to a coroner, who is likely to hold an inquest.
In Britain, coroners usually hold inquests to determine the facts of unexplained, sudden or violent deaths.