Her body has been taken to a hospital in nearby Dartford, Kent Police said today.
"Arrangements are in hand for the post-mortem to be carried out tomorrow at the hospital," police said in a statement on Tuesday local time.
"After the results of the post-mortem have been received, the coroner will officially open an investigation and decide whether an inquest is necessary."
In her last Twitter message on Sunday, Peaches posted a photograph of her as a toddler being held by her mother, with the words, "Me and my mum".
Her father Bob, who put together the huge Live Aid rock show in 1985 to raise money for the Ethiopian famine, said: "We are beyond pain.
"She was the wildest, funniest, cleverest, wittiest and the most bonkers of all of us.
"How is this possible that we will not see her again? How is that bearable? We loved her and will cherish her forever."
Pop stars, presenters and even presidents have voiced their shock at her death.
Irish President Michael D. Higgins, who began a state visit to Britain on Tuesday, was due to meet Dublin native Bob Geldof during the trip.
"I extend my deepest sympathies to Bob Geldof and his family on the sudden and untimely death of his daughter Peaches," he said.
"This is such a difficult cross to bear for any family and all of our thoughts are with Peaches' family and friends at this time."
Peaches' children are the third generation to have lost their mother young. Geldof's own mother died of a brain haemorrhage when he was seven.
Peaches was the second of Geldof and Yates' three daughters. Geldof also adopted her half-sister, Tiger Lily - Yates's daughter with late INXS frontman Michael Hutchence.
Peaches had a media career writing for British newspapers and presenting celebrity-driven television shows.
She married her first husband, rock musician Max Drummey, in 2008 but they separated the following year.
Peaches wed her second husband Tom Cohen, a rock singer, two years ago. They had two sons, Astala and Phaedra.
Peaches' former publicist Ray Levine, told the BBC that she was "a very endearing, charming young lady".
"She didn't actually like being in the spotlight so she had to learn that because of who she was and the way that she lived her life it was something she would have to accept and deal with," he said.
"And in the end she did that and she embraced it."