6:18 A.M. PDT -- The inquest into Geldof's death just ended in Kent. Coroner Roger Hatch says the post mortem shows Geldof used heroin shortly before she died ... and that the drug is "likely to have played a role in her death." Hatch also said Peaches' body was found on her bed by her husband.
Peaches Geldof died as the result of a heroin overdose ... according to a London newspaper that says the cause of death will be officially revealed tomorrow at an inquest.
Geldof -- daughter of rocker Bob Geldof -- was found dead in her Kent home April 7. Authorities called it a "non-suspicious, unexplained sudden death" ... but an autopsy proved inconclusive because the coroner didn't have the results of the toxicology tests.
The Times of London reports the tox report will show she died from an overdose of heroin. Geldof's mother, Paula Yates, died from an accidental heroin overdose in 2000.
The Times' report angered a Kent city official ... who told TMZ the toxicology results were supposed to be confidential until tomorrow's inquest, saying "if I find out who leaked it I will cut their balls off."