As it nears a week since the last sighting of British backpacker Grace Millane, the leader of a trust set up to help families in crisis is urging her family not to give up hope.

Millane was last seen entering a downtown Auckland hotel with a man last weekend.

More than 24 police officers have been investigating the 22-year-old's disappearance since she was reported missing four days ago and those investigations have now included questioning the man with Millane when she was last seen.

Police say they have "grave fears" for her safety and are searching for clues in a room at the hotel.

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Matt Searle from the Lucie Blackman Trust had been in discussions with Millane's family and said their hopes of finding her was still intact.

The Lucie Blackman Trust acts to support British nationals in crisis overseas - often dealing with the families of missing people.

The trust was set up by the father and sister of Lucie Blackman - a British national who disappeared, and was later found dead, when she was working in Tokyo.

Searle said Millane's family were doing everything they could to bring her home and were grateful for the huge response from Aucklanders who knew of the situation.

"They're obviously feeling absolutely devastated, distraught and terrified," he said.

"It's a very scary thing to go through, which so few of us can understand."

Searle said he was impressed with how well the family was holding up.

Searle described the trust as a "logistical best friend" that helped families with missing people .

While looking for clues could feel like a "needle in a haystack", Searle said all it could take is one piece of intelligence to bring that needle out and guide police on their next move.

He urged anyone who might have relevant information to get in touch with police.

"We deal with hundreds of cases every year, we get over 3000 inquiries just about missing British Nationals every year."

Searle said there were a lot of situations that ended well.

"There's often an extremely strange or bizarre explanation, but nonetheless they end in a happy reuniting for the family.

"It doesn't necessarily look bad. It doesn't look brilliant and it doesn't look good, and obviously it's concerning the longer it goes on for."

The family "mustn't fear the worst", he said, as families were sometimes reunited after weeks, months, or even years.

Detective Inspector Scott Beard told media yesterday that sighting was on CCTV at the CityLife Hotel on Queen St at 9.41pm on December 1.

David Millane spoke to media at a police press conference about his missing daughter. New Zealand Herald Photograph by Doug Sherring
David Millane spoke to media at a police press conference about his missing daughter. New Zealand Herald Photograph by Doug Sherring

"At present we have spoken to a person and we still have no evidence of foul play."

He wouldn't be drawn on whether Millane knew the man before their meeting at CityLife and, in response to questions, described the man as a "person of interest".

An apartment at the hotel was also being treated as a place of interest, he said.

A scene examination at the hotel is continuing today.

Millane's father, who arrived in New Zealand yesterday, also spoke to media.

"We are staying very positive in the search for our Grace and we all hope she returns home soon to her family," he said in a further release today.