So far 23 people have tested positive for the virus at a caravan park in Craven Arms, and several people raised concerns about not being able to get tests.
Shropshire Council has said that an issue with the phone booking system has been resolved and Craven Arms residents can get tests if they call the NHS 119 number.
A testing site was set up at Craven Arms Business Park on Saturday and is open for the next two weeks every day from 10.30am-3.30pm. Testing is by appointment only, and residents are being asked to book an appointment via NHS Test and Trace online or by ringing 119.
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Jean MacDonald had difficulties trying to get a test in Craven Arms on Monday, so ended up booking a home delivery test.
She said: "I live in the town and I use a local shop so I thought I would get myself tested. I phoned the NHS 119 number as advised in the Shropshire Star article. But the lady who answered said she had got no record of there being an outbreak in Craven Arms.
"Then she said I should call back next week to book an appointment.
"I was really taken aback by the response. I think it's disgusting to be told to wait a week. I was really angry about it. I thought it was bizarre."
The council insisted the issue is resolved and people can book tests. Rachel Robinson, Shropshire Council's director of public health, said: “Cluster outbreaks are not uncommon during a pandemic and we would like to reassure people that the risk is still very low. We are continuing to provide Long Lane residents on-site support, as well as guidance to help keep them and their loved ones safe.
"Our priority remains protecting the health and wellbeing of all residents in our community. Anyone who has a fever, persistent dry cough, or loss or change in their sense of taste or smell should go online to arrange a test or call 119.”