The inquest, held at Wem Coroner's Court, heard that Mark Stevens, 47, from Bridgnorth, died six days after he was held in a Shrewsbury police cell for more than 14 hours.
Mr Stevens was rushed to the Royal Shrewsbury Hospital after his condition deteriorated, leaving him in a drowsy state with slurred speech and hallucinations.
He lost consciousness soon after his arrival at hospital, thought to be due to a morphine overdose.
Mr Stevens had a cardiac arrest on July 8 and died three days later.
Shropshire coroner Mr John Ellery told a jury of six men and four women that medical experts considered his death was due to hypoxic brain injury caused by cardiac arrest and an overdose of the medicine Zoromorph, administered by a doctor.
Mr Stevens, who had been an alcoholic, suffered from diabetes type 1, hepatitis C and pancreatitis for which he was taking strong painkillers. He was also taking diazepam, for alcohol withdrawal symptoms and mirtazapine for depression. Mr Stevens had brought his medicines with him.
However Dr Christopher Lisk a retired forensic medical examiner, was asked by Mr Ellery to carry out a review of the care Mr Stevens received at the police station.
He criticised the actions of three members of staff from Medacs, an independent healthcare agency, custody nurse Karen Taylor, Dr Shiraz Budhani and Dr Malcolm Awty, who are both forensic medical examiners.
Nurse Taylor, who will give evidence on Thursday, had asked for an ambulance to be called soon after she arrived at the station on the morning of July 6, 2011.
Mr Stevens' family thanked custody sergeant Edward Hancox for the care he gave their brother in calling for an ambulance when his condition deteriorated.
The inquest continues.