Nine Covid-19 cases have been now been confirmed among production staff at Wensleydale Creamery.
Three more positive tests have been recorded after six cases were announced by the Hawes business last week.
The creamery is still operating but some areas have been “restricted” while the outbreak is brought under control, bosses say.
All production staff have now been tested for coronavirus.
Several members of staff are isolating as a result of their colleagues’ positive tests.
Jill McMullon, chair of Hawes and High Abbotside, said there have been concerns in the local community that the site was still open despite the outbreak.
She said the community had also raised concern with her about transparency and the lack of information coming from the business about the outbreak.
She added: “A lot of people think that the site should be shut, but if Public Health England say it doesn’t need to be then we’ve got to go with that.
“Because Public Health England, the county council and the district council are fully aware of the circumstances, we’ve got to trust what they’re doing to ease the situation is correct.”
Residents have also voiced concerns about creamery staff, who they believe should be self-isolating, continuing to visit shops and businesses in the town.
One resident, who asked not to be named, said: “It is incredibly frustrating to see a Wensleydale Creamery worker who has been told to self-isolate out shopping in Hawes on Market Day.”
Dr Lincoln Sargeant, director of Public Health for North Yorkshire, says there is a low risk to the general public following the Covid-19 outbreak.
He said the Wensleydale Creamery had worked “very openly” with North Yorkshire County Council and with other agencies including Public Health England to get this outbreak quickly under control.
“Speedy joint action means we can stop the virus from spreading and protect visitors, staff and the wider community. We commend them for their efforts to ensure measures are in place to keep staff and visitors safe.”
A spokesperson for the Wensleydale Creamery added: “Our fast response in collaboration with Public Health England and North Yorkshire County Council meant we were able to test all members of our production team, advise further members of staff to isolate as a precaution and ensure additional important measures were quickly put in place to contain the spread of the virus.
“Public Health for North Yorkshire has praised our quick response and the additional robust and responsible measures implemented by the Wensleydale Creamery to operate safely and ensure the safety of our colleagues.”
Bosses say the Wensleydale Creamery Visitor Centre is unaffected and remains fully open with “stringent procedures in place to ensure a safe and welcoming environment for visitors and staff”.
The spokesperson added: “Since our phased reopening, we have controlled customer and staff numbers, maintaining 2m social distancing in all areas, undertake frequent comprehensive cleaning, introduced one-way systems with separate entrances for each area, with hand sanitisers throughout, and daily temperature checks for employees. We are also operating track and trace.
“We look forward to welcoming visitors for a safe and enjoyable day out at our visitor centre, including Calvert’s Restaurant and the 1897 Coffee shop which are participating in the government’s Eat Out to Help Out Scheme.”