The mum-of-two was found at her home in Wroxham, Kent on Monday, and police have said her death is being treated as "non-suspicious" and "unexplained".
"Officers continue to investigate the circumstances surrounding the death in order to compile a reports for the coroner," a spokesperson said. "The result of a toxicology report can take several weeks."
On Wednesday, Peaches' father Bob Geldofflew back to the UK from America to reunite with his heartbroken family, including Peaches' husband Thomas Cohen and grandchildren Astala, 23 months, and Phaedra, almost one.
He issued an emotional statement following his daughter's death.
Bob Geldof flew back from the US after receiving the news of Peaches' death
"Peaches has died. We are beyond pain," he said. "She was the wildest, funniest, cleverest, wittiest and the most bonkers of all of us.
"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.
"Tom and her sons Astala and Phaedra will always belong in our family, fractured so often, but never broken."
In his own statement, Peaches' husband added, "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."