Commander Neil Basu has made a statement on behalf of the Metropolitan Police, following an IPCC report on the murder of Sally Hodkin by Nicola Edgington.
He said: "The death of Sally Hodkin is tragic and our thoughts go out to her family and to Kerry Clark who was injured by Nicola Edgington.
"Mrs Hodkin had been on her way to work in the early hours of Monday 10 October when she was approached by Nicola Edgington and stabbed in the neck. Edgington also assaulted Kerry Clark.
"Prior to this, Edgington was voluntarily taken by police to the A&E department of Queen Elizabeth Hospital, Woolwich and was waiting to be seen by a mental health team.
"The officers left her in a place of safety to be cared for by professionals trained to deal with people with mental health issues, and the IPCC investigation found that this was the correct course of action.
"Edgington made a number of calls to police from hospital asking for officers to attend whilst she was in the mental health assessment unit waiting to be assessed. She was reassured that she was in a place of safety and would be assessed by medical professionals.
"Police control room staff made contact with the hospital who advised that the hospital security had the matter in hand and that there was no need for police attendance.
"There has been criticism that officers did not conduct a Police National Computer (PNC) check on her details, which would have identified that Edgington had been violent in the past and had a previous conviction for manslaughter.
"With the benefit of hindsight this may have assisted officers with background information, however, as the IPCC investigation concluded, whilst Edgington was vulnerable, she was compliant and herself seeking medical assistance.
"The officers acted on the facts in front of them, which they do on a regular basis every day.
"A PNC check alone would not have prevented the actions that Edgington subsequently took.
"The IPCC concluded their investigation and no recommendations were made for either misconduct or learning for the MPS. They also identified that no police officer or staff breached the code of conduct or MPS policies.
"Despite this we will of course review the findings of the IPCC investigation.
"Once again our thoughts remain with the family of Sally Hodkin and with Kerry Clark."
Local police in Greenwich were not notified that Edgington was living in the area.
Police and police staff did not carry out a police national computer check on Edgington which would have alerted them to her previous conviction for manslaughter.
Officers missed an opportunity to use their powers under the Mental Health Act when Edgington tried to leave an A&E department shortly after she arrived with police.
Edgington's second 999 call from an A&E department was downgraded because she was considered to be in a place of safety and an officer was not asked to return despite Edgington saying she could be very dangerous.
The police only contacted the hospital after a fourth call had been received.
John Cooper, QC, mitigating, said she was a woman in crisis and had not been given the help she asked for.
But the Recorder of London Judge Brian Barker said Edgington should stop blaming others for her actions and take responsibility.
He jailed her for life with a minimum term of 37 years for murder and gave her a concurrent sentence of life with a minimum term of 20 years for attempted murder.
Judge Barker told 32 year old Edgington that her behaviour had been "consistent and calculated".
He said: "You are manipulative and exceptionally dangerous. What you did could not have been more selfish. I disagree that the responsibility for these acts can be laid on others. You made your choice and these were terrible acts for which you must take responsibility.
You have come as near as can be to having three deaths on your hands."
Miss Clark had escaped only with cuts to her hands because of her bravery and quick action, he said.
IPCC commissioner Sarah Green said it was of "great concern" that police did not carry out a PNC check.
"This tragic case has robbed a family of a much-loved wife, mother, grandmother and friend and my thoughts again go out to Sally Hodkin's family," she said.
"Nicola Edgington had a violent history linked to her mental health problems and was evidently aware that she was a threat to others.
On Monday 10 October 2011, she made repeated phone calls to police asking to be sectioned under the Mental Health Act and warned officers in person of the risk she posed to those around her.
While our investigation found that no police officers or staff breached the code of conduct, it is of great concern that no PNC check was carried out which would have immediately alerted them to Edgington's violent history.
Without this PNC check, both the police and staff at Queen Elizabeth Hospital, Woolwich were without crucial information which may have influenced their future decisions, increased the urgency of the situation and could have escalated the medical attention she was given."
Nicola Edgington, 32, made five 999 calls on the day of the attack asking to be sectioned under the Mental Health Act because she believed herself to be a danger.
But hours later she was still at large and took a knife from a butcher's shop before she almost decapitated grandmother Sally Hodkin, 58, and attempted to murder Kerry Clark, 22.
The 2011 killing, in Bexleyheath, south-east London, came after Edgington - who now faces life in prison - was released back into the community in 2009.
An investigation by the Independent Police Complaints Commission (IPCC) found local police in Greenwich were not notified that she was living in the area after an order for her indefinite detention was lifted.
The watchdog also found Met staff failed to carry out a police national computer check on Edgington when she made contact with officers on October 10 2011, shortly before the murder.
This would have alerted them to her previous conviction for the manslaughter of her mother in 2005, the IPCC said.
Hours before she killed, Edgington sought help at a local hospital from where she called 999.
But after delays in admitting her, she walked out.
The IPCC found officers only contacted the hospital following her fourth phone call and said Edgington's second 999 call from the A&E department was downgraded because she was considered to be in a place of safety.
An officer was not dispatched at this stage despite Edgington's claim she could be very dangerous, it found.