The 25-year-old died in her family home last month while alone with one of her two young sons and an inquest was told on Thursday that forensic tests found heroin in her system.
The police also said Geldof's husband of two years, musician Thomas Cohen, was not under suspicion in her death or their concurrent investigation into the supply of drugs.
"Inaccurate reports have also been made suggesting that no drugs paraphernalia was found at the address, with suggestions that the scene had been 'tampered' with prior to police arrival," Detective Chief Inspector Paul Fotheringham said in a statement.
"To prevent further speculation I will confirm that contrary to rumour in the media my officers did seize drugs paraphernalia from the address on 7 April."
Geldof, a media and fashion personality, was the second of Irish musician and campaigner Bob Geldof and Paula Yates's three daughters. Yates died from a heroin overdose in 2000, three years after the death of INXS singer Micheel Hutchence, for whom she had left Bob Geldof.
The Thursday inquest heard Peaches' body was found by Cohen, in a spare bedroom of their home in Wrotham, Kent, in southern England in the afternoon of Monday, April 7.