Balfour Beatty has closed the structure that supplies the Hinkley Point C nuclear power plant.
A time of in-depth cleaning of the facility is planned this week after the first one held last weekend.
Christina Gray, director of public aptitude at Bristol City Council, the measures in place “would prevent the epidemic from spreading into the community.”
Six other tests were shown after 22 cases were announced on Monday.
Gray said that everyone who tested positives isolate themselves and that the quest for touch continues.
“Balfour Beatty reacted quickly, ended voluntarily to lessen the threat of infection, and called public fitness experts.
“These actions, as well as the ones we are taking now, will involve this epidemic and prevent it from spreading in the community,” he said.
Balfour Beatty stated that he had initiated the NHS testing and tracing procedure and that “lately he had not demonstrated that any had an effect on the site of the main structure of Hinkley Point C.”
“We continue to interact with everyone involved and remain committed to the health, protection and well-being of everyone who paints with us and for us, as well as the general public,” said one spokesman.
The 28 positive tests at Avonmouth are more than the ones recorded by the entire city of Bristol last week.
Figures as of Monday showed 18 new cases in the week leading up to July 23, about 3.9 for another 100,000 people, up from 8 in the past week.
New instances in Avonmouth will be counted in total Bristol if staff live in the city.
Unite’s regional manager, Heathcliffe Pettifer, said the union had asked Balfour Beatty to reassure himself about the measures to prevent him from threatening further transmissions once he returned to the site.
“We also ask Balfour Beatty to ensure that all workers, whether hired directly through Balfour Beatty or through a contractor, receive full payment for site closure,” he added.