Hundreds of tests for the South African variant of Covid-19 are waiting to be analysed, two weeks after emergency surge testing was carried out.
More than 9,000 people who live or work in Maidstone were tested.
But only 70 of the 400 that came back positive for Covid-19 have been fully analysed for the variant, according to figures from council officials.
No cases of the variant have yet been found, and the Department of Health said "further data will be provided".
But the leader of Maidstone Borough Council, Martin Cox, says he is "frustrated" by the speed of the analysis, known as sequencing, and the lack of results.
He said: "It is a frustrating situation. What we find difficult to understand is why we have to wait this length of time.
"We were told this was an urgent process. We got all that testing done, we sent them all off, and then we waited, and we waited a bit more.
"We only know that a quarter of the tests have gone on to be sequenced."
By Mark Norman, Health Correspondent, BBC News South East
Two weeks ago there appeared to be an urgency about the need to identify any new cases of the South African variant in the ME15 postcode.
At short notice, police officers, Kent Fire and Rescue crews and local community wardens were drafted in to knock on doors offering ten thousand Covid-19 tests to people on their doorsteps.
But two weeks later and that urgency seems to have faded with politicians and public health officials still waiting for the results and still unsure if there is a problem in their community.
Experts locally are frustrated at the delay and are concerned that public health decisions are being taken without all the evidence available.
Targeted surge testing began on February 2 in the ME15 postcode, after a case of the South African Covid-19 variant was discovered.
Andrew Scott Clark, director of public health at Kent County Council, said the sequencing was important to understand if there is an issue with the variant locally.
"We need to make sure that we have the right strategy in place and know what we need to do if we find the South African variant," he said.
A number of other areas underwent surge testing for the South African variant, including parts of London, the West Midlands and some Bristol postcodes.
A spokesperson from the Department of Health and Social Care said: "Additional surge testing and sequencing is being deployed in a number of targeted locations to help control and suppress the spread of detected Covid-19 variants, while enabling better understanding of these variants."