Detectives are trawling through her mobile phone records, e-mails and diaries as it appears she kept her drug use hidden from her husband, 24-year-old Thomas Cohen, reported daily Express.
Peaches, who died from an overdose of heroin, also visited a drug rehabilitation centre in Maidstone, Kent, wearing a hoodie to avoid being recognised, and without her husband's knowledge.
The hunt was launched after drug paraphernalia was found at her 1 million pounds home in Wrotham, Kent.
Detective Chief Inspector Paul Fotheringham said, "I would like to make it clear that Thomas Cohen is not in any way under suspicion. We are in regular contact with both sides of the family to keep them apprised of our progress."
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The full resources of the Serious Crime Directorate - elite detectives from Kent and Essex - have been deployed.
They include officers with a knowledge of criminals who supply drugs to wealthy users in London and the Home Counties.
Peaches, 25, had become noticeably thinner in the weeks before she died.