A grandmother would not have been murdered in Bexleyheath if mental health staff had assessed the danger posed by a mentally ill woman properly, a coroner has concluded.

Paranoid schizophrenic Nicola Edgington virtually decapitated Sally Hodkin, 58, with a butcher's knife in a random attack six years after killing her own mother.

The now 38-year-old murdered the law firm accounts clerk after attempting to kill artist Kerry Clark, 22, on October 10, 2011 after suffering a relapse in her mental state.

She had earlier walked out of a hospital mental health unit unchallenged after repeatedly calling police to beg for help and telling A&E staff she felt like killing someone.

Edgington was taken to Oxleas House in Woolwich but soon walked freely out of a door which should have been locked to commit the killing, coroner Sarah Ormond-Walshe said.

Sitting at South London Coroner's Court, she concluded on Thursday: "I find that there was a failure to assess her properly, failure to risk-assess her properly, and failure to put her on one-to-one observations.

"I find that there was a failure to ensure that she be prevented from leaving Oxleas House if she attempted to do so.

"Had one or more of these failures not happened, the death of Sally Hodkin would not have happened."

The coroner recorded a verdict of unlawful killing at the conclusion of the two-week inquest, saying that Mrs Hodkin would have died instantly from incised wounds to the neck.

Ms Ormond-Walshe went on: "She was waiting to be shown her bed, waiting in an unlocked area of Oxleas House being observed on 15-minute undocumented observations when she absconded.

"She had had no sleep, was very agitated, had not been taking her anti-psychotic and mood-stabilising medication and had probably also taken skunk."

In 2009, Edgington was discharged from the Bracton Centre mental health facility after just three years to live in the community - despite an order she be detained indefinitely after killing her mother Marion.

In the months and weeks before the killing, a series of events identified as major risk factors contributed to a collapse in Edgington's mental state, the inquest previously heard.

Around two weeks beforehand, Edgington believed she had suffered a miscarriage, which was significant because she had a termination against her will shortly before killing her mother.

The inquest also heard Edgington threatened at least two people with knives after her discharge.

Speaking after the inquest, Mrs Hodkin's son and solicitor Len Hodkin, 42, standing with his brother Ian, 41, said: "There were clear failings by the multidisciplinary team in the weeks and months leading up to this.

"If she was recalled to hospital a lot sooner she would not have been on the streets to kill our mum."

Her care team gave evidence at the inquest defending her release and saying they followed correct procedure.

Asked by the coroner if she would take the same steps if faced with the same scenario again, her psychiatric nurse and care co-ordinator Tanya Biebuyck said: "Considering the clinical picture, yes, we made the right decisions.

"I think it's difficult to say we could have made any other decisions given her mental health stability, co-operation with her care plan ... there was no evidence of any changes in her mental health."

Edgington was found guilty at the Old Bailey in 2013 of murdering Mrs Hodkin and attempting to murder Miss Clark and was jailed for life with a minimum term of 37 years.