Chief public health officer Professor Nicola Spurrier says her number one priority today is to gather more resources from the Commonwealth and interstate to speed up testing, as fatigue sets in across overrun stations around the state and people are turned away.

Australian Defence Force personnel and teams from interstate will be brought in, doctors and nurses will be relieved from Adelaide hospitals to administer testing and GPs will be given broader abilities to swab.

Authorities also hope to soon publish live wait times for testing sites, expand opening hours of clinics and set up a dedicated site for high-priority cases.

It comes as the state entered its first day of a week-long lockdown and recorded a new case overnight – a woman in her 20s who was working at The Greek on Halifax St restaurant exposure site in the city on Saturday night and who is also a staff member at Westminster School in Marion.

Dozens more exposure sites have now been added to the growing list, including Westminster School at Marion, Burnside Shopping Centre at Glenside, Tea Tree Plaza Shopping Centre at Modbury, St Ann’s College at North Adelaide, Whistle and Flute café at Unley, McDonalds at Felixstow and Woolworths at Marryatville.

Spurrier told reporters a short time ago the latest case was at Westminster School on Monday for a teacher-training day. It was a pupil free day so students weren’t on site but a number of teachers have now been placed in quarantine.

The woman provides counselling to boarders at the school and authorities are now checking if any of them were exposed.

She also went shopping at Burnside Village on Sunday, which is why that is now an exposure site.

Spurrier said authorities were most concerned bout two “high risk” exposure sites – The Greek on Halifax restaurant in the city and Tenafeate Creek Wines at Yattalunga.

Asked if there was a potential seventh case – connected to the winery at Yattalunga – Spurrier said “all I can say is I’ve been told by the team before I came to the press conference that they are calling this a high-risk site”.

Emergency financial help is also being made available to South Australians affected by the shutdown, with the Commonwealth announcing payments for people in Adelaide and the State Government announcing support for people in the regions.

The cluster began when an 81-year-old man tested positive at Modbury Hospital on Monday morning.

His daughter and other close contacts in the north-eastern suburbs have since tested positive, with one of those exposing diners at the busy Greek on Halifax city restaurant on Saturday night.

Spurrier said genomic testing from the 81-year-old matched with the New South Wales outbreak.

The man did his 14-day quarantine period in NSW after returning from Argentina, before arriving in Adelaide on July 8 and spending more than a week in the community before developing symptoms and testing positive.

Will Richards, 21, was one of hundreds of South Australians caught up in testing queue chaos this morning.

He went to the Firle testing station at 7am with his household after learning his mother was at the Marryatville Woolworths exposure site.

They waited two and a half hours before being told by officials they weren’t going to get tested by the 5pm closure time.

“The line was massive and there were cars parked in all of the side streets everywhere,” he told InDaily.

“We found the back of the line and then we were waiting there for about 2.5 hours. We moved about 10 metres in that time.

“Then a government car came and said we wouldn’t be able to get tested because apparently someone parked their car at 3am and everyone parked behind that thinking it was the queue so then there were cars parked everywhere, no queue, just in a circle, so we got told we weren’t going to get tested by 5pm.

“They said the line wasn’t really going anywhere.

“They could have just had signs in place for queuing. They must have known there were going to be so many people queuing up to get tested.”

The family then headed to the Mt Barker testing station where they have been told there is a six-hour wait standing up and they can’t guarantee they’ll get tested before the closure time.

The state president of the Australian Medical Association, Dr Michelle Atchison, was also caught up in queue chaos.

She joined the lengthy line at Victoria Park about 10pm and tweeted early this morning that she was still waiting at 5am.

“Get more resourcing out there SA Health,” she said.

“We don’t want even one person giving up and going home.”

Other medicos faced the same problem, with doctors’ union president Dr David Pope concerned about the bigger impact on the health system.

“Essential healthcare workers are having great difficulty and long delays in accessing COVID testing,” Pope tweeted.

“This needs to be addressed urgently otherwise essential health services are left unstaffed or staff work with symptoms of possible COVID.”

Spine surgeon Dr Mike Selby tweeted that he was required to have a COVID test but by the time he had finished an urgent surgery there were queues five-hours long.

“What facilities are there for healthcare workers and essential workers that have jobs to do in the morning?” he asked.

Premier Steven Marshall acknowledged the “massive sacrifice” and “frustration” from South Australians caught up in extensive lines at testing sites and said his government was doing “everything we can” to add more resources.

“Today we will be pulling every single lever possible to increase the capacity to provide that (testing) service,” he said.

Marshall reminded people there were 86 testing sites across the state and urged people to check the SA Health website for their closest.

“What we are trying to do today is to further increase the swabbing staff to decrease the inconvenience to the people of SA,” he said.

“We don’t want anybody turning away in frustration. I know there have been delays.”

He said staff from blood collection clinics and elective surgery would be diverted to clinics to boost testing.

He also said more toilets would be opened around the particularly busy 24-hour Victoria Park testing station.

Spurrier said she had spoken with ADF surgeon general Sarah Sharkie about getting support to help with overrun testing clinics.

She said ADF personnel based in Adelaide would begin helping today, while personnel from interstate would be brought in soon.

Extra local nursing staff were also being made available to help with swabbing.

More than five thousand South Australians have now been placed into quarantine.

SA Police Commissioner and state emergency coordinator Grant Stevens said QR codes would now be included in rideshare vehicles, taxis and public transport to help with contact tracing.

“The more data we can collect the more effective we can be for contact tracers,” he said.

Stevens said anecdotally people had been doing the right thing on day one of the lockdown which he hoped would not have to be extended beyond seven days.

He said some small police stations would close for the lockdown so officers could be diverted to COVID duties.