Duncan Larcombe, former royal editor at The sun newspaper, said her 14-year-old daughter was among those who received an incorrect result.
Maidstone’s public relations director Kent told BBC News his family was taking this “very seriously” and her two children had been kicked home from school to isolate themselves.
Mr Larcombe said the incident, which kept him from working, called into question whether the testing system was adequate.
He told the broadcaster: “The whole economy depends on the competence of the testing labs and if they don’t do their job, they have to be held accountable. “
His daughter was able to take another test on Thursday which was negative, but given that Kent was just placed at level 3, Mr Larcombe wondered if the ‘government modeling was flawed’.
A spokesperson for the Department of Health and Social Affairs (DHSC) said it was an “isolated incident” and all those affected would be asked to have another test.
They added that this was due to a “problem with a batch of test chemicals” and that the problem would be fully investigated.
DHSC did not specify whether the error affected regional infection rate figures.
Test and Trace has been plagued by problems, with figures earlier this week revealing that around four in 10 contacts of those who have tested positive for the virus are still not reached.
The Prime Minister on Monday announced an additional £ 7 billion for Test and Trace in his winter plan, with the aim of increasing testing and improving contact tracing.
It brings the overall funding provided for Test and Trace this fiscal year to £ 22 billion – nearly a fifth of the entire annual NHS budget – which has been criticized.
But Boris Johnson insisted the system offered “value for money”, although he admitted there had been “starting issues”.