People began reporting issues booking tests in Lincolnshire last week after the government chose to prioritise more capacity in the worst affected areas.
Many people were being sent for a test to Leicester and Oldham, Nottingham or Chesterfield. Home testing kits were also quickly taken.
However, people have been able to get tests by turning up at the Showground site north of Lincoln, where they would fill in a form to get tested.
Lincolnshire’s assistant director of public health Tony McGinty said there had been no changes to the situation over the weekend and there was no indication it is likely to improve in the county.
“We don’t have any fixed detail on when that’s likely to improve.
“The national lab system has brought some more capacity online and is planning to do more capacity over the coming weeks, but I think we’re going to have restrictions for a few weeks at least now.”
He continued to urge people only to book a test if they had clear symptoms or had been asked to do so until the situation improves.
Health Secretary Matt Hancock last week said around 25 per cent of people getting tests had been “just to check” or as pre-holiday precautions.
In Lincolnshire, 8,000 tests were carried out in the first week of September.
If Mr Hancock’s figures are reflected in those, it would mean that around 2,000 people in the county were getting tested unnecessarily.
Those that cannot get tests straight away are advised to keep trying for two to three days.