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."
More top news
Police investigating the murder of a grandfather from West Ham have arrested a second man on suspicion of murder.
Police are appealing for information after a woman was killed and three people injured after a crash in east London.
A restaurant where pets and their owners can share a meal together has opened just in time for Valentine's Day.