Boris Johnson came under concerted pressure to take action to tackle male violence and misogyny and make the UK safer for women, as the discovery of human remains in the search for Sarah Everard caused an outpouring of anger.

The inquiry into the disappearance of the 33-year-old marketing executive added poignancy to the annual International Women’s Day debate in the House of Commons as dozens of female MPs told moving and angry stories of the harassment they had been subjected to.

They also called for tougher action from the government when the police, crime, sentencing and courts bill returns to the House of Commons next week.

Labour MP Jess Phillips read out the names of 118 women killed by men since last year’s debate.

The government is yet to publish a long-promised strategy on tackling violence against women and girls. The prime minister’s spokesperson said on Thursday that ministers hoped to do so by the end of the year.

The home secretary, Priti Patel, responding to the many women who have shared personal experiences in the wake of Everard’s disappearance, said she could relate to their stories.

The home secretary said: “These are so powerful because each and every woman can relate. Every woman should feel safe to walk on our streets without fear of harassment or violence.”

The Labour leader, Keir Starmer, speaking at a campaign event, underlined the scale of the problem – and urged men to call out abusive behaviour.

“If we are to really confront this the first thing we need to do is to recognise the scale of violence against women and girls. And I’m not sure everybody appreciates just how prevalent and pervasive it is,” he said.

“We all need to tackle this at root; we all need to recognise the issue and challenge behaviours,” Starmer added. “I think there’s a particular issue for men. It’s very important for men to speak out on this issue.”

A recent survey by UN Women UK found that 97% of women aged 18-24 had been sexually harassed, while 80% of women of all ages said they had experienced sexual harassment in public spaces.

The government will face cross-party pressure to use the crime and sentencing bill to take tougher action on crimes against women, when the wide-ranging legislation returns to the House of Commons next week.

The Guardian understands Labour’s Harriet Harman will urge the government to enshrine the victim’s right not to have their previous sexual history cross-examined in court, an amendment that has widespread cross-party support.

The government was also challenged by the Lib Dems’ Wendy Chamberlain to make misogyny a hate crime as part of the domestic abuse bill.

A cross-party amendment supported by a string of charities, including the Fawcett Society and the Jo Cox Foundation, would make all police forces in England and Wales record misogynistic crimes as hate crime, a campaign started by the Labour MP Stella Creasy. The amendment will be voted on in the House of Lords next Monday.

“The challenge to the government is – pass the domestic abuse bill – it’s been in the offing for four years. Legislate to make misogyny a hate crime. Make sure that those occupying positions of trust are people we really can trust,” Chamberlain said.

Speaking in the debate, Phillips said it was abhorrent that the government still did not collect detailed data on the numbers of women killed each year and the circumstances of their deaths.

“In this place we count what we care about, we count the vaccines done, we count the number of people on benefits, we rule or oppose based on a count and we obsessively track that data,” she said. “However, we don’t currently count dead women … Dead women is this thing we’ve all just accepted as part of our daily lives. Dead women is just one of those things. Killed women are not vanishingly rare – killed women are common.”

Phillips, who has made it a tradition to read the names at each year’s IWD debate, said she was indebted to the work of Karen Ingala Smith and the Counting Dead Women project who compiled the list.

Harman, who is mother of the house as the longest serving female MP, criticised the words of the Met police commissioner, Cressida Dick, who said abductions of women on the street were rare – though acknowledged the fear many women would be feeling.

The former Tory cabinet minister Maria Miller said Everard’s disappearance had “sent shockwaves around the UK” because many women could relate her last movements to their own regular routine.

“For many women this news story will bring back memories of threatening situations they found themselves in, through no fault of their own, being sexually harassed on the streets walking home from meeting friends, anonymous threats of physical violence on social media, sexually assaulted in plain sight in rush hour and public transport on the way to work,” she said.

The former Conservative cabinet minister Andrea Leadsom, said the strength of feeling merited cross-party action. “I feel angry that women walking home in the dark have to be scared of the person walking closely behind them and sad because for far too many women even getting home safely doesn’t mean they’re safe from harm. So I say to all colleagues right across the house, let’s never let party politics get in the way of protecting women and girls.”

Labour’s Rosie Duffield, who spoke last year of her own experience of domestic abuse, said there had been an “outpouring of collective rage over the last 24 hours” and compared the anger to the Black Lives Matter protests.

“Sarah Everard has reignited a fire within us, much like George Floyd did. Enough is enough. We must take a long hard look at society, at social media, at misogyny, at ourselves. And let’s hope that next year’s list is virtually non existent,” she said.

Marsha de Cordova MP, the shadow women and equalities secretary, criticised the minister for women and equalities, Liz Truss, for not attending the debate, leaving Maria Caulfield to give the government’s response.

De Cordova described the debate as, “the first time since the beginning of this pandemic that ministers have put aside time to talk specifically about women”, and called it “unacceptable” that Truss had not attended.

A spokesperson for the Government Equalities Office said Truss had an immovable diary commitment, but had contributed heavily to Caulfield’s speech.