Specialised units to tackle violence against women must be introduced in all police forces in the wake of Sarah Everard’s death, a Conservative peer whose cousin was murdered by a "local sex pest" has urged.

Baroness Gabby Burton, who sat on the scrutiny committee for the Domestic Abuse Bill, said it was "shocking" that not all forces had departments trained to deal with these crimes given their prevalence.

The former press secretary to David Cameron spoke out after Met PC Wayne Couzens pleaded guilty to murdering Ms Everard, who was kidnapped in London while walking home alone at night earlier this year.

Baroness Burton revealed that her own cousin was killed by a man who was, until then, considered no more than the "local sex pest".

She said she believes the murder could have been prevented if police had taken the perpetrator’s less violent behaviour more seriously.

"You don’t generally wake up and become a murderer or rapist, you work up to these things," she told the BBC.

"’Low-grade crimes’ are not necessarily low-grade at all and must be taken very seriously because very often these criminals go on to murder and rape, they’re working up to that moment. Harassment in the street should be taken very seriously.

"I lost my cousin 30 years ago. She was essentially murdered by the local sex pest. She was 18, didn’t really know him, but she had caught his eye. He was on the police radar but they weren’t really taking it very seriously. This was in a suburb of Paris.

"Of course you can’t help thinking that if they had taken that harassment and casual leering at women in the street more seriously, perhaps my cousin would have been alive today.

"It is right that police up and down this country look at their culture and say ‘if a woman comes into our police station and reports a crime, are we taking the right action, definitely not dismissing her, are we believing her, are we doing everything we can to make sure justice is found?’

"One very important point that police forces up and down the country must take on board is training, specialist training, making sure their first responders do understand the nuances around sex crimes, domestic abuse crimes, and there are specialist units."

‘More women will die senseless, avoidable deaths’

Jamie Klingler, who was at the forefront of the movement to reclaim the streets in the wake of Ms Everard’s death, said the justice system must be reformed to better capture the "sliding scale" of violence against women.

Since Ms Everard’s murder in March, 52 more women in Britain have been killed in circumstances where a man was the principal suspect.

“In every single one of those 52 cases and sadly, as we now know, in Sarah’s too, there will have been an escalation of behaviour," she said.

“I am no psychologist, but it must be vanishingly rare that a man goes from having no track record of violence, deviance or abusive behaviour whatsoever to killing a woman.

“There is always a sliding scale, and until our justice system starts to really understand that and take that seriously, I fear that more women will die senseless, avoidable deaths.”