Shutting the investigation after 15 months, officers have told her dad Sir Bob “all lines of enquiry were exhausted”.
But no arrests were made.
He had been away for the weekend with Astala, now three, leaving his wife at home with Phaedra, two.
Police found 6.9g (0.24oz) of “importation quality” heroin stashed in a black cloth bag inside a cupboard over a bedroom door with a purity of 61 per cent, worth between £350 and £550, her inquest heard.
The syringe containing the fatal dose was discovered in a cardboard box next to Peaches’ bed, which also contained candies.
An inquest into her death found there was no evidence her death was deliberate.
The socialite died of a heroin overdose in 2014 but the case of who supplied her the Class A substance has now been shelved after police confirmed “all lines of inquiry were exhausted”. Police said at the time that her death was being treated as “non-suspicious but unexplained and sudden”, but the results of a toxicology report later showed Geldof had heroin in her system. She was 41 and her daughter was just 11 years old.
Geldof’s mother, Paula Yates, was also found dead of a heroin overdose at her home in London in 2000 when her Peaches was 11.
In a television interview past year, Geldof’s father, Sir Bob Geldof, the lead singer with the Boomtown Rats and noted anti-poverty campaigner, said he “blames himself” for her death, saying: “You’re the father who is responsible and clearly failed“.
Over a year on, the Kent and Essex Serious Crime Directorate have now released a statement updating their investigation.
“I would like to take this opportunity to pay tribute to Peaches’ family who have supported our inquiries during what has been a hard time”, he said. She had always informed him they had been clear, and Cohen now said he believed Geldof had lied about the results of the tests.