Police forces should be compelled to deal with violence against women and girls with the same level of resources, expertise and urgency as terrorism or organised crime, the victims commissioner for England and Wales has said.

After Sarah Everard’s killer was given a full-life sentence on Thursday, campaigners said there was increasing frustration and the time for action was now.

Vera Baird said violence against women and girls should be made a strategic policing requirement to give the issue central direction and extra resources, particularly for specialist officers, so there was “no doubt what obligations the police have towards victims”.

She said: “There are many unanswered questions about how violence against women and girls is policed and I think if we have this clear requirement it sends a clear message that tackling it is a priority.”

Baird said requirements on agencies to fully investigate and take action in cases of violence against women could be included in the victims bill, which the Guardian understands was ready to be consulted on before the new justice secretary, Dominic Raab, took up his post.

“​​Without that it will just muddle on, being ignored as if it were a low-level crime,” she said. “We have seen in this awful case that what is seen as low-level offending against women and girls can mark out a predatory attitude to them which can speedily escalate if not tackled.”

The Labour leader, Keir Starmer, led calls for an inquiry into how Everard’s killer, Wayne Couzens, a Metropolitan police officer who had been reported for indecent exposure on three occasions, “slipped through the cracks”. “[We] have to understand why that happened, and whether there were any assumptions made when his previous wrongdoing was looked at,” he said.

The Labour MP Yvette Cooper went further, calling for a full independent investigation into violence against women and girls within the police service.

The home secretary, Priti Patel, said there were “serious questions that need to be answered by the Metropolitan police” while giving her backing to the Met commissioner, Cressida Dick.

The director of the Good Law Project, Jolyon Maugham, called for a public inquiry into “how cultural failings by the police and the broader criminal justice system contribute to the murder or rape of tens of thousands of women a year”. He said: “Enough really is enough. How many more women must die?”

Baird’s call echoes the recommendation of a damning root-and-branch examination by Her Majesty’s Inspectorate of Constabulary and Fire & Rescue Services (HMICFRS), which found “problems, unevenness and inconsistencies” in dealing with the “epidemic” of violence against female victims in the UK.

It was published as news emerged that Sabina Nessa, a primary school teacher, had been found dead in a park close to her south London home. A man has appeared in court accused of her murder.

According to the Counting Dead Women project, run by Karen Ingala Smith, 80 women were killed between the deaths of Everard in March and Nessa on 17 September.

Campaigners in the sector said there was a growing sense of anger and frustration that promises of change were not resulting in greater safety for women.

Farah Nazeer, the chief executive of Women’s Aid, said a public inquiry into men’s violence against women and girls would probably expose other institutional and government failings but was unlikely to lead to the action needed.

There was already a wealth of evidence and recommendations in the Inspectorate of Constabulary report, the government’s recently published Violence Against Women and Girls (VAWG) strategy and rape review, Nazeer said. “We all know what needs to be done. But making it a matter of priority, choosing to prioritise funding into this area, choosing to make that cultural shift – these are political choices that we’re not making.”

Women’s groups welcomed what some saw as an increased level of restraint in the reporting of Couzens’ trial, with many publications choosing not to feature a prominent photograph of the murderer, while BBC Radio 4’s Today programme chose to mention Couzens by name sparingly in its reporting on Thursday and included the full victim impact statement of Everard’s mother, Susan.

“We find that women’s experience is lost so often when we talk about the impact of male violence against women and girls,” said Jayne Butler, the chief executive of Rape Crisis England and Wales. “We welcome that some outlets have chosen to focus their coverage on Sarah.”

Andrea Simon, the director of the End Violence Against Women coalition, said that despite the reviews and promises of change since Everard’s murder, little had changed.

“Violence against women and girls is at an epidemic level, the police inspectorate has said the whole system needs an overhaul, the government has already apologised for the shameful low rates of prosecution of rape. What more do we need to uncover? We actually just need to move to doing something about it,” she said. “We’ve had all of these reviews, and we’ve seen no material change. We need to get on with actually making a difference now.”

The minister for safeguarding, Rachel Maclean, said the government was committed to radically changing how violence against women and girls is tackled with a whole-system approach. She said the VAWG strategy published this summer set out “the government’s ambition to increase support for survivors, bring perpetrators to justice, and, ultimately, reduce the prevalence of violence against women and girls.”