Robert Napper, 29, had pleaded not guilty to the murders of Samantha Bisset, 28, and her daughter Jazmine in November 1993, but guilty to their manslaughter on grounds of diminished responsibility. His pleas were accepted by Mr Justice Hooper at the Old Bailey.
Detectives have examined possible links between the Napper case and the murder of Rachel Nickell on Wimbledon Common, south-west London, and Scotland Yard said it retained an "open mind'.
The court was told by Nigel Sweeney, for the prosecution, that when Napper got into the Bissets' one-bedroom basement flat in south-east London, he killed Miss Bisset in the hallway by stabbing her eight times in the neck. Then he sexually assaulted and suffocated Jazmine in her bed, before dragging her mother into the living room where he mutilated her body.
Miss Bisset's body was found by her boyfriend, Conrad Ellam, when he visited the flat the following morning, the court was told, and two large- scale police operations were launched which eventually resulted in Napper's arrest.
On 10 March the previous year, Napper - armed with a lock-knife - attempted to rape a young woman in Hither Green. When she resisted, he became angry and beat her, before escaping. Eight days later, he stalked a woman near fields in Eltham and attacked her at knife-point. Both women later identified Napper. He was also identified by tests on his semen.
Two months later, Mr Sweeney said, Napper followed a woman as she pushed her two-year-old daughter in a buggy, then raped her.
Napper first appeared at the Old Bailey last week to stand trial after denying the double murder. But Mr Justice Hooper was concerned about his fitness to plead, and said yesterday: "There were five psychiatrists who had reached the conclusion he was suffering from schizophrenia or something similar. But this defendant did not accept he was suffering from a mental illness."
The judge said that to send Napper to hospital without limit of time would enable "this grossly psychotic and ill man to be treated in a condition of maximum security for as long as was deemed necessary".Reuse content