A poll of 1,699 adults by YouGov, on behalf of the End Violence Against Women (EVAW) coalition, found 47% of women and 40% of men polled said trust in the police has dropped since the details of Couzens’ crimes became public.
Nearly one in three women (29%) said they continue to trust the police despite his actions.
Couzens will spend his life in jail after he abducted, raped and murdered 33-year-old Ms Everard near Clapham Common in south London in March while a serving officer in the Metropolitan Police.
The atrocity sparked a widespread public outcry, and a Government crackdown on sexual harassment as part of its strategy to tackle violence against women and girls.
Home Secretary Priti Patel also promised a “thorough review” of police vetting.
The poll suggested three quarters of women (76%) said they felt the culture of policing has to change in order to better tackle violence against women and girls.
Andrea Simon, EVAW director, said: “The police and Government response to legitimate public outpourings of anger and distress about police failings have fundamentally missed the mark.
“We are yet to see any commitment and accountability for the meaningful internal work needed to shift the institutional cultures and practices that excuse and enable this harmful behaviour – instead we have seen superficial and unevidenced measures announced that feel like a PR exercise.”
Couzens used his police warrant card and handcuffs to kidnap Ms Everard as she walked home.
Sentencing him, Lord Justice Fulford said that Couzens’s abuse of his position as police officer was a key factor in his decision to deliver a whole life tariff.
But last month, Couzens was reported to be appealing his sentence.