Brian Vale, 45, suffered from a psychopathic personality disorder. He repeatedly banged Dr Ann Mead's head onto the pavement after she ended their six-month affair.
Dr Mead, 35, a hard-working and popular GP, was desperate to find a husband with whom to settle down and have children, the court was told.
Vale, an unemployed, lonely man with three broken marriages, pleaded guilty to the manslaughter of Dr Mead on 13 October last year.
His plea of not guilty to murder on the grounds of diminished responsibility was accepted by the Recorder of London, Judge Lawrence Verney QC.
He said Vale, a former civilian worker at Islington police station, posed a danger to women for an 'unpredictable period of time' and the judge had passed a life sentence because of the 'exceptional' circumstances of the case.
John Nutting, for the prosecution, told the court that Vale, of Bethnal Green, east London, fell madly in love with Miss Mead and wanted to marry her, but she regarded him as suitable only for a casual relationship.
He 'snapped' and attacked her outside her pounds 150,000 Georgian flat in Grove Park, Herne Hill, south London, banging her head against the pavement and her garden wall for between 15 and 20 minutes before leaving her body lying by the roadside.
Later Vale told detectives: 'I didn't really want to hurt her. I loved her. But she didn't love me.'
Mr Nutting said Dr Mead was a 'popular and successful' GP working at a shared practice in Herne Hill.
'The one sadness in her life was that at the age of 35 she had not found anyone with whom to share her life. She wanted to have children and expressed fears that she may never achieve that particular goal,' Mr Nutting said.
'She wanted to settle down and was looking for a husband.' She gave her 'predicament' careful thought and, after consulting a friend, decided to advertise in the New Statesman lonely hearts column on 7 May last year.
She received six replies - one of them was from Vale.
Their meetings often ended up in bed, the court heard, but the relationship soon began to go wrong.
'Tragically, they were looking for different things in the relationship. She just wanted someone to see occasionally. He wanted something much more permament and long lasting,' Mr Nutting added.
A judge yesterday expressed concern that delays in obtaining medical reports prevented him passing sentence on the obsessed killer of the student Catherine Ayling.
Curtis Howard, an American, stalked Miss Ayling, 24, for two years before stabbing her to death, dumping her body in the boot of his hire car at Gatwick airport and flying back to the US.
Howard admitted manslaughter on the grounds of diminished responsibility when he appeared at Lewes Crown Court earlier this year.
Mr Justice Hidden, sitting at the Old Bailey, had to postpone sentencing Howard, 27, in July and again yesterday because the medical reports were not ready.