The defendant wore a grey tracksuit and appeared to have a red wound on the top of his forehead.
Couzens spoke only to confirm his name and personal details, sitting between two plain-clothes officers in the dock and leaning forward for most of the hearing.
Chief Magistrate Paul Goldspring asked prosecutor Zoe Martin to give a brief summary "given the nature of the case and the interest".
The court heard the officer is accused of kidnapping Ms Everard in the Poynders Road area of Clapham.
Ms Martin said Ms Everard was reported missing by her boyfriend on 4 March and that a body discovered on 10 March in a wooded area of Ashford, Kent, had been formally identified as the missing woman using dental records.
A post-mortem examination has taken place but no cause of death was given in court.
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Before his court appearance, Scotland Yard said that Couzens, of Deal in Kent, was taken to hospital for a second time in 48 hours on Friday for treatment to another head injury sustained in custody, before he was discharged and returned to a police station.
He was previously treated in hospital for a separate head wound on Thursday, also sustained in custody when he was alone in his cell.
Meanwhile, police in dry suits were seen on Saturday continuing to search around the area where Ms Everard's body was found near Ashford.
Metropolitan Police Commissioner Dame Cressida Dick visited search sites in Kent to thank the teams involved in continued searches in relation to the investigation into the 33-year-old's murder.
Sarah Everard's body found in builder's bag and identified using dental records, court told - LBC