Wayne Couzens, 48, pleaded guilty to murder Mme Everard, 33, at the Old Bailey on Friday.
The Independent Office for Police Conduct (IOPC) later revealed that 12 Metropolitan Police officers are under investigation regarding the Everard case.
But the Met and Kent Police are under increasing pressure to reveal how Couzens, who previously admitted to kidnapping and raping, was not questioned further on three separate complaints of indecent exposure that date back to 2015.
The IOPC is investigating the Kent force into the 2015 incident, while two officers are questioned about two similar incidents in London in February of this year.
Ms Everard, whose death sparked large-scale protests against women’s safety, was abducted on her way home in the south of the capital on the night of March 3.
His body was found near land belonging to Couzens in Kent a week later
Harriet Wistrich, director of the Center for Women’s Justice, wants a full public inquiry into “police misconduct and misconduct” around the Ms. Everard case.
“As the protesters have made clear, women do not feel safe and it is incumbent on the government and all criminal justice agencies to now take action against the epidemic of male violence which is the other crisis of public health of our time, ”she said.
Shadow Home Secretary Nick Thomas Symonds is also urging the Met to review its verification process.
The Labor MP said: “It is absolutely vital that everything is done so that this never happens again.
“The Metropolitan Police and the Police at large must examine the control processes and their own protection systems to ensure that those who pose a threat to the public are not able to occupy such vital positions of trust. . “
The police commissioner she met, Dame Cressida Dick, said she felt “disgusted, angry and betrayed” over Couzens’ calls and apologized to the Everard family.
The 12 Met agents who received notices of misconduct include one who was still on probation and shared an inappropriate graphic regarding the case with agents on social media before setting up the cordon at the scene of the search.
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Couzens is to be sentenced after a two-day hearing that will begin on September 29.