The death of British backpacker Grace Millane has rocked tourists travelling in New Zealand.

Tourists staying at Base Backpackers Hostel in central Auckland, where 22-year-old Millane had been staying, told the Herald of the sorrow that has settled in at the popular travellers' quarters.

Max Parmentier, a Belgian tourist staying at Base, said he had shared a dorm room with Millane and was "really sad" to hear of her death.

"I didn't talk much with her but she seemed like a really gentle girl and really cool," he said.

"For me, I am really sad that she has died. How can you think that she has gone for a party for her 22nd birthday and then she just disappeared for a few days. We had no idea what had happened."

Millane, from Essex, had been travelling around New Zealand as part of a year-long OE and arrived in Auckland on November 30.

The next night she was captured on CCTV footage entering the CityLife hotel in the CBD with a 26-year-old man.

He allegedly murdered Millane sometime that night, or the next day - which was her 22nd birthday.

Nine days later her body was found in an area of bush in West Auckland's Waitakere Ranges.

Tourist Max Parmentier who has been staying at The Base Backpackers met British backpacker Grace Millane during her stay before she was killed. Photo / Greg Bowker

The alleged killer appeared in court today, as a post mortem examination was carried out to establish when and how exactly Millane died.

Parmentier said Millane's death had made him "worried for other people".

"I want to say to people to be careful, but at the same time I don't want to say it as you don't want to scare everybody," he said.

A female Swedish tourist, who wished to remain anonymous, said the alleged murder had made her more wary about travelling alone.

"I think it is horrible. It's really sad but unfortunately it happens a lot," she said.

"I have travelled to Australia and New Zealand by myself and have heard of it happening in Australia as well.

"It makes me more wary of travelling alone. As a girl you have to be careful going places alone with someone you don't know, or walking home from work and stuff."

A female German tourist, who also wished to remain unnamed, said she had come to New Zealand thinking it was a "very safe country" but was now "a bit afraid".

"It is very scary that something like this has happened," she said.

"We have been here for five days, the two of us. We feel safer being together, but I have travelled alone before - but I would never go with a man I don't know."

Prime Minister Jacinda Ardern said earlier today that Millane should have been safe in New Zealand.

Ardern addressed media this afternoon for her post-Cabinet press conference and said New Zealand was normally a safe place to travel in.

She said there was an overwhelming sense of shame that this tragedy happened in New Zealand, and she apologised to the family on behalf of New Zealand.

Millane's father David, a millionaire property developer, flew to New Zealand on Friday.

He later spoke to media and described his daughter as a "lovely, outgoing, fun-loving, family-orientated daughter".

Two days later, Grace Millane's body was found in the Waitakere Ranges.

The 22-year-old's body was believed to have been taken to the bush in a rental car that was later found in Taupo.

While finding her body and making an arrest may seem like the closing of the case, police still have weeks if not months of hard work ahead.

The team behind Operation Gourami - the investigation into Millane's murder - is now tasked with building a case against her alleged killer in a bid to secure a conviction.