The murder of the British backpacker Grace Millane has provoked an unprecedented outpouring of collective shame and grief in New Zealand, and sparked a national conversation about violence against women.

The Grief Centre in Auckland said many New Zealanders were experiencing “vicarious trauma”, exacerbated by the country’s small size.

In the days following Millane’s death, radio shows have been flooded with callers speaking of their sorrow. The prime minister, Jacinda Ardern, and other MPs have paid tribute to the 22-year-old and spoken of how her death has appalled residents.

Play Video 1:14 Jacinda Ardern: 'Hurt and shame' over Briton's death – video

Lucy, 33, from the South Island, said she and her friends were feeling “overwhelmed” by Millane’s murder. She has cried at work, in her car, while at the supermarket, in the shower and in bed.

“As a New Zealander, it fucking sucks that it happened here. She should have been safe here. It’s not something that she should have had any fear about. You can’t live your life worrying that ‘I shouldn’t meet a stranger because they might murder me’. It’s not a feasible way to live your life,” she said.

“Girls will see this news about Grace and not feel safe anymore. It’s another reminder that as women and girls you’re just not safe, that men can be violent to you anywhere … And all the privilege in the world isn’t going to stop that.”

Millane disappeared in Auckland on 1 December. Her body was found in dense bushland in west Auckland a week later. A 26-year-old man was charged with her murder and is on remand, to appear in court in late January.

Jan Logie, the parliamentary undersecretary for domestic violence and sexual violence issues, said she wondered “if some of the strength of our reaction is about how inured we have become to the quite horrific things that happen in our society. Then [we] welcome someone into our house and it happens to them and we get to see the everyday reality writ large and it shocks us.

Facebook Twitter Pinterest Grace Millane, who disappeared on 1 December. Photograph: Lucie Blackman Trust/PA

She said Millane’s murder had sparked a national conversation about the country’s rates of violence against women.

New Zealand has one of the worst rates of family violence in the Organisation for Economic Co-operation and Development, an intergovernmental organisation with 36 member countries. Police attend a domestic violence incident every four minutes, with an estimated 80% of incidents going unreported.

The majority of domestic violence incidents involve violence towards women, and one in three New Zealand women report experiencing some form of abuse from a partner.

Data from the ministry of justice shows about 1 million New Zealanders, or 23% of the population, are directly affected by family violence every year.

Logie said she hoped the national revulsion over Millane’s murder would translate into action. “People’s strong emotional responses offer us the opportunity to make fundamental changes in our country that we know we need. I want people to hold on to this feeling, this anger.”

Grief counsellors said Millane’s death had provoked a widespread and collective experience of sorrow and distress in a country where people were typically reserved in their emotional displays outside the sporting arena.

Dr Peter Bray, a British expat who leads the counselling programme at Auckland University, said Millane’s death had shaken New Zealanders’ world view and exploded the myth of the country as a peaceful South Pacific idyll.

“In a sense, New Zealanders view each other as family, and something awful has just happened to a member of our extended family,” said Bray, who added he too had found himself impacted and unusually “struck” by the murder.

“We are an island nation and our children travel abroad a lot and we want them to be looked after. And when we can’t do that for other people’s children – even by default – that really affects us. There is a sense at the moment that we are not able to trust the world, and that comes as a real shock for New Zealanders – the world is not how we once thought it was.”

The Grief Centre’s general manager, Trudie Vos, said there was a “sense of shock and shame, clients are coming in and are really struggling with it”.

She said New Zealanders were relatively “dulled” to the emotional impact of domestic and family violence in the country because it was so common, but Millane’s murder had resonated with so many people because stranger murders were uncommon

“Personally I believe it is good that we’re shocked, that we’re saddened and that we express it. The general lack of emotional expression by New Zealanders contributes to the serious mental health problems we have in this country,” Vos said.

“New Zealanders are not used to experiencing loss and sharing it with themselves and others – Grace has changed that.”