The boss of the health trust that treated Nicola Edgington said today it was "a matter of extreme regret" that she was able to leave a mental health unit on the day of the stabbings.
But chief executive of Oxleas NHS Foundation Trust Stephen Firn said that a report into her treatment found that the decision to let her live in the community in 2009 was sound.
He also insisted that the care she received afterwards was "good quality", despite the fact that she stopped taking her medication.
Mr Firn said: "I am very sorry that this tragic incident happened and would like to express again my sincere condolences to the family of Mrs Hodkin. We completed a thorough investigation with a panel which included an independent Consultant Forensic Psychiatrist and a representative of our elected governors.
"The trust inquiry report concluded that the decision to recommend to the Ministry of Justice that Nicola Edgington was discharged from the Bracton Centre in 2009 was sound and the care she received in the community following her discharge was of good quality."
However he admitted that it was "a matter of extreme regret" that Edgington was able to leave mental health unit Oxleas House on the morning of the stabbings.
He went on: "It also concluded that the decision taken to admit Nicola Edgington to Oxleas House was appropriate. It is a matter of extreme regret that she was able to leave the unit before being admitted and subsequently carried out this dreadful crime.
"The report makes several recommendations which have all been put into place and reviewed regularly by the Board of Directors. In line with national NHS requirements there will now be an independent inquiry."
A Ministry of Justice spokeswoman said: "The decision to discharge Nicola Edgington in 2009 was made by officials, without reference to ministers, under authority which is delegated as a matter of routine by the Secretary of State."
Nicola Edgington, 32, pinned grandmother Sally Hodkin, 58, to the ground and slashed her throat with a butcher's knife.
Moments before, she had attacked artist Kerry Clark, 22, at a bus stop but fled when she was disarmed.
Edgington, of Greenwich, south east London, was found guilty of murder and attempted murder by a jury at the Old Bailey.
The prosecution said she was suffering from a borderline personality disorder and her actions were deliberate.
But the defence argued that she was mentally ill with schizophrenia and her responsibility was diminished.
In 2006, she was ordered to be detained indefinitely under the Mental Health Act for killing her mother Marion, 60, the previous year.
She had stabbed her nine times after returning to the family home in Forest Row, Sussex.
By 2009, Edgington was released to live in the community while being monitored by a doctor, nurse and social worker.
But as her private life began to unravel, Edgington was unable to cope as she stopped taking her medication, the court heard.