Published: 11:30, 23 July 2014
Read our live updates from this morning's inquest below. Reporting: Thom Morris and Kiran Kaur
DCI Paul Fotheringham revealed to the inquest the full detail of the last moments Peaches Geldof was alive.
His full report to coroner Roger Hatch has now been released by Kent Police.
You can read it by clicking here.
Tom Cohen - the 24-year-old widower of Peaches Geldof and father of her two sons - is pictured leaving the inquest.
Wearing sunglasses, he left the Old Town Hall in Gravesend by a back door.
He had given evidence to the inquest, telling the coroner of the devastating moment he found his wife dead at home surrounded by drugs paraphernalia.
Peaches Geldof's death was a cruel echo of her own mother's tragic fate more than a decade earlier.
Paula Yates, 41, was found dead at her home in London of a heroin overdose.
Just hours before her death, Peaches posted a childhood picture of her and her mum on Twitter and Instagram with the comment: "Me and my mum".
Tom Cohen has left Gravesend Old Town Hall via the back entrance after standing as a witness at his wife's inquest.
Kent Police have released a statement on the investigation into who supplied the heroin to Peaches Geldof.
A statement said: "An investigation into who supplied the heroin to Ms Geldof-Cohen is ongoing. To date no one has been arrested or interviewed under caution in connection with this."
The hearing has now concluded and Peaches' widower is expected to leave shortly.
Coroner Roger Hatch concludes: "The death was drugs-related".
He expresses his sympathy to Peaches' family.
Mr Hatch said it was "clear" she had been taking heroin from drugs paraphernalia around her.
He added: "By early February, Mr Cohen had found messages on her telephone that indicated she was using drugs and she retrieved the drugs from the loft and disposed of them down the toilet."
All three witnesses have now finished giving evidence and coroner Roger Hatch is beginning his summing up.
He says it is clear she had been taking a strong level of heroin, but her tolerance to this level had declined.
To recap for those just joining us, the inquest has heard Peaches Geldof had been a heroin addict and had been taking the substitute drug methadone in the two-and-a-half years before her death.
Mr Fotheringham: "27 methadone bottles were found around the family home. There is an ongoing police investigation to find out who supplied them.
"Recent puncture marks were found on the inside of her elbows and her left arm."
He concludes Peaches died of a heroin overdose, based on his evidence.
Mr Fotheringham: "The original assessment of the scene supported my early hypothesis that Peaches had taken heroin."
The court is told 34 medical syringes were found by forensic teams.
Around her body was drug paraphenalia - tights, spoons, a cap from syringe, resin from heroin. In another bag in the house, officers found 6.9g of heroin.
Heroin found in the house was 61% purity and worth £350-£550, the inquest heard.
DCI Paul Fotheringham, from Kent Police, stands as a witness.
He begins to tell the court about Peaches' actions in the lead up to her death.
She was wearing a grey dress and long-sleeved striped top.
Coroner: "It's right that Peaches Geldof had been a heroin addict. Is that correct?"
Tom Cohen: "Yes"
He added the he found her in the spare bedroom they used "when the kids were sleeping"
Mr Cohen took a seat after answering a series of questions and was comforted by the person next to him, who put his arm around his back after standing as a witness.
Husband Tom Cohen introduces himself to the court as he stands as a witness.
Wearing a black waistcoat and white shirt, with his hair in a pony tail, he prepares to relive the moment he found his wife's body.
Pathologist Peter Jerreat has arrived in court as a witness. He has begun describing the state in which Peaches was found at her Fairseat Lane home.
Mr Jerreat said: "The brain was slightly swollen due to a lack of oxygen to the brain but all other internal organs were normal."
He revealed puncture wounds had been found on her body - wrists plus thumbs.
Evidence of codine, methadone and morphine were found in her blood. Methodone had come from heroin, with levels well within the fatal range.
She died of a heroin overdose, the inquest told, with the cause of death given as opiate intoxication.
The court has been told to rise as coroner Roger Hatch has arrived to begin the inquest.
Just moments before, Peaches' husband Tom Cohen took a seat in The Grand Hall to hear details of his wife's death.
The first row of chairs in The Grand Hall has been reserved for family members, although there aren't any seated yet.
Peaches's husband Tom Cohen arrived at about 9.10am, but it is not known if other relatives are present.
Journalists and Kent Police officers have been invited into the Old Town Hall 15 minutes before the inquest is due to begin.
The inquest will be held in the Grand Hall, on the upper floor, where three rows of chairs have been set aside for observers.
The inquest is expected to give more details on the mother-of-two's death at her home in Fairseat Lane, Wrotham, on April 7.
The 25-year-old was found dead on the edge of a bed in the spare room by Tom, who had been staying with his parents in London.
A police operation saw the house and grounds searched, with "drugs paraphernalia" discovered.
We're at Gravesend Old Town Hall, where we expect the full inquest into Peaches Geldof's death to begin at 10am. It will be held by coroner Roger Hatch and will last around 90 minutes.
Peaches's husband Tom Cohen arrived about 20 minutes ago. It is not known if her father Bob Geldof is due to attend. Around 30 members of the Press are waiting outside.
It was at this town hall back in May at the opening of the inquest that police first revealed heroin was likely to have played a part in Peaches' death - prompting comparisons with her mother Paula Yates' drug overdose death in 2000.
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