A Christchurch father is frustrated his 14-year-old daughter was turned away for a vaccination jab after Prime Minister Jacinda Ardern said teens could join their parents.

The announcement was made at the Government's 1pm press conference on Thursday that parents can book their child's, if they are over 12, Covid vaccine from this morning.

Any parent already booked in could also take their child along at the same time, Ardern had said.

Richard, who did not want his last name used, said he and his daughter were told at the Pages Rd clinic this morning that September 1 was the earliest she could get a jab.

He said it's frustrating because they had been talking to their daughter about keeping to her bubble and taking no risks.

"I listened to the briefing and was pleased they were expanding it out to 12 to 15-year-olds.

"I was a little sceptical that I could just rock up with my daughter but the Prime Minister said if you've already booked just bring them along so I thought cool," he said. 

The Pages Rd testing clinic in Christchurch on Friday. Photo / Hamish Clark

A little more clarity from the Government would be great, he said.

A Ministry of Health spokesman says centres will do everything to accommodate teens who don't have bookings, but it may not always be possible.

At the 1pm update on Friday, Director-General of Health Ashley Bloomfield said there were a number of people turning up with 12 to 15-year-olds for vaccinations.

He said people planning to bring children with them should phone ahead as many sites had limited space.

Covid-19 testing centres in Christchurch have seen a large increase in demand since the country entered lockdown with staff reporting Wednesday was the busiest day since the original outbreak last year.

Community-based testing centres in Canterbury conducted 10 times the number of tests on Wednesday as they did the same day last week.

They conducted 1119 swabs for testing compared to 110 swabs last Wednesday.

Those figures exclude routine surveillance testing of border workers and swabs taken by general practices - their tests bring the total number to 3000 in Canterbury.