Peaches Geldof died from an overdose at her home in Kent, UK, in April 2014. She was 25.
Bob Geldof’s daughter had been a heroin addict and took the substitute drug methadone for two years before her death.
Detectives said they had “exhausted all lines of inquiry” trying to find out who supplied her with the Class A drug.
Detective Superintendent Paul Fotheringham said the case would be reviewed if further information or witnesses came forward.
“I would like to take this opportunity to pay tribute to Peaches’ family who have supported our inquiries during what has been a difficult time,” he added.
A police search of her home at the time of her death found 6.9g of heroin but there was no indication she had planned to take her own life, an inquest last year heard.
Peaches Geldof’s husband, Tom Cohen, told the hearing she started using the drug again in February 2014.
The musician, who had been away for the weekend with the eldest of their two sons, said he became concerned when she failed to answer her phone and found his wife slumped on the bed upon his return.
Coroner Roger Hatch said Peaches Geldof’s death had been “drugs related” and expressed his deep sympathy to her family.
Peaches Geldof’s mother, Paula Yates, died of a heroin overdose at the age of 41 when Peaches was 11 years old.
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