Her birthday was on Sunday but she didn't contact her family.
Tony McLeod, British High Commission Wellington consular manager, said the commission was aware of the missing person report.
Mr Beard said various sightings have her wearing either a black top, blue jeans and red sneakers, or a black dress with white shoes.
"We are asking anybody who has been in contact with her or knows her to contact police".
She was last seen on Saturday about 7.15pm around SkyCity.
Grace's father is due to arrive in New Zealand on Friday, reports Stuff.
It remains unclear if Grace returned to her hostel after the CCTV picture was taken and the senior cop confirmed some of her belongings are still in her room, which she had been sharing with at least four other people.
Ms Millane had been travelling alone in New Zealand for about two weeks, and was staying at Base Backpackers hostel in Auckland city centre.
"Please, please pick up the phone and get in touch - we are really anxious about you", he added.
They became anxious when she failed to reply to birthday messages on Sunday.
Her family raised the alarm two days later, after she stopped responding to their messages. The contact with us stopped on Thursday. Prior to then she had been in contact daily.
Newstalk ZB reporter Chelsea Daniels attended the Police press conference and told Larry Williams the longer it carries on without any sightings, the more worrying it is.
'Her family member is coming out - obviously, they're distraught.
Beard said it was understood Grace had a New Zealand and an English cellphone.
Grace Millane hasn't been in contact with her family for five days. It has been shared thousands of times around the country.
Police in New Zealand are continuing their search for the missing woman from Wickford.
Det Insp Scott Beard, of Auckland City Police, said more than 20 staff were working on the case.
Ms Millane had previously written on social media.
Grace Millane had been in New Zealand for about two weeks.
The investigation so far had concentrated around Millane's movements since she arrived in New Zealand, he said.
Ms Millane graduated from the University of Lincoln in September and planned to travel around the world.