Geldof was pronouced 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 presenter.
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.
Police are treating her death, mourned by stunned friends and family, 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.