Johnny Sleigh (36) failed to return home from an evening at a nightclub.
Concerns about him were raised on Monday after he failed to return messages left on his phone and did not turn up for work.
By Tuesday, friends reported his disappearance to the police.
Metropolitan Police Detective Sergeant Stephen Marshall said police were in the middle of their inquiries but "everyone in the department had dropped everything" to work on the investigation.
Mr Sleigh, a draughtsman at an engineering firm, was last seen at the Brazilian-themed Guanabara Club in Holborn, where he had gone with friends on Friday night.
It is understood he stayed on after friends left about 12.30am on Saturday.
He never arrived back at his flat in Clapham Common, South London, which has since been searched by police.
Mr Sleigh has been based in London for six years.
He was planning to return home at the end of this year, most likely to live in Auckland.
He kept in regular contact with his family in New Zealand through Facebook and text messaging.
His last contact with them was via Facebook on Wednesday last week and he spoke to his mother on the phone about three weeks ago, saying everything was fine.
His sister, Catherine Booth, of Timaru, said the family were contacted by friends on Tuesday.
"The family are in shock and are extremely worried for Johnny's safety," she said, adding it was completely out of character for Mr Sleigh to disappear.
Mr Sleigh's four siblings have joined their parents, Peter and Caroline Sleigh in Waimate, to lend each other moral support and try to decide whether any family representatives should travel to London in the next few days.
Mrs Booth said it was difficult to know what to do.
The police had advised them the investigation had only gone "full steam ahead" in the last day and they were still collecting information from such sources as phone accounts, bank accounts and closed circuit television footage from the club.
They have also taken Mr Sleigh's laptop and documents from his home.
Police had pointed out family members could miss out on vital information which might be uncovered in the 24 hours it took to fly to Britain.
"It is hard being so far away from where he was last seen." While it was difficult having to deal with the publicity, the family hoped it would help trigger the memory of someone who might have seen Mr Sleigh.
Mr Sleigh was brought up near Waimate.
He attended Waimate High School and then completed a forestry degree through Canterbury University.
He later got engineering qualifications and undertook draughting training in Brisbane.
Close friend Martha McKenzie-Minifie, also based in London, said this was "very unlike Johnny".
"His friends and workmates here in London and his family back in New Zealand are very worried. There are a lot of questions and very few answers at the moment."
Ms McKenzie-Minifie said she had been working with friends to ring hospitals, visit the club with Mr Sleigh's photograph and gather contact details for anyone who may have spoken to him in the days before his disappearance.
She said Mr Sleigh had been taking salsa lessons at the club and visiting it on Friday nights for about six weeks.
He was familiar with the local area and lived only about 10km away, so it was unlikely he had got lost.
His friends have started a Facebook page called "Please Help" in the hope of gaining information.
His family is appealing for anyone with information to contact London's missing persons unit or the New Zealand police.
- The New Zealand Herald/Otago Daily Times
