NHS Test and Trace is believed to have suspended testing operations provided by the Immensa Health Clinic Ltd at its laboratory in Wolverhampton.
It follows an investigation into reports of people receiving negative PCR test results after testing positive with a lateral flow test.
While investigations are underway into the precise cause, NHS Test and Trace estimate that around 400,000 samples have been processed through the lab, the vast majority of which will have been negative results, but an estimated 43,000 people may have been given incorrect negative PCR test results between September 8, and October 23, mostly in the South West of England.
The UK Health Security Agency says the issue at the Wolverhampton laboratory is an "isolated incident" and there are no technical issues with the lateral flow devices or PCR test kits themselves.
The number of tests carried out at the Immensa laboratory are small in the context of the wider network and testing availability is unaffected around the country, the UK Health Security Agency says.
Dr Jenny Harries, the head of NHS Test and Trace, has said it is "not clear yet" what went wrong in the private laboratory that has stopped operating due to fears people were given the wrong test results. She insists, however, that the "rest of the system is working as normal".
Dr Harries, who is also head of the UK Health Security Agency, says there will be "a serious incident investigation" within the organisation.
"I want to make sure if there are any further problems with other laboratories we can absolutely spot them as quickly as possible, so I will be conducting a serious incident investigation within the Health Security Agency to make sure we can mitigate any problems going forward," she says.
Dr Will Welfare, public health incident Director at the UK Health Security Agency (UKHSA), said: "We have recently seen a rising number of positive LFD results subsequently testing negative on PCR.
"As a result of our investigation, we are working with NHS Test and Trace and the company to determine the laboratory technical issues which have led to inaccurate PCR results being issued to people.
"We have immediately suspended testing at this laboratory while we continue the investigation.
"There is no evidence of any faults with LFD or PCR test kits themselves and the public should remain confident in using them and in other laboratory services currently provided. If you get a positive LFD test, it’s important to make sure that you then get a follow up PCR test to confirm you have COVID-19. If you have symptoms of COVID-19, self-isolate and take a PCR test."
Andrea Riposati, CEO of Immensa Health Clinic Ltd, said: "We are fully collaborating with UKHSA on this matter. Quality is paramount for us.
"We have proudly analysed more than 2.5 million samples for NHS Test and Trace, working closely with the great teams at the Department of Health and Social Care (DHSC) and UKHSA. We do not wish this matter or anything else to tarnish the amazing work done by the UK in this pandemic."
John Denley, Wolverhampton's director of public health, said: "We have been made aware that NHS Test and Trace has suspended one of its privately-run PCR testing laboratories.
"NHS Test and Trace estimates that 43,000 people, mostly in South West England, may have been given incorrect negative PCR test results by the laboratory in Wolverhampton between September 8, and October 12.
"Test and Trace will contact people that could still be infectious to advise them to take another test, while close contacts who are symptomatic will also be urged to get tested. If you are not contacted, you should continue to follow the advice you have already received.
"Wolverhampton Council has no involvement with this privately-run laboratory, but we are seeking urgent clarification from the UK Health Security Agency and the Department of Health and Social Care as to whether the issue is likely to have implications for residents who have taken PCR tests in Wolverhampton over the last few weeks.
"In the meantime, people with symptoms of Covid-19 should continue to book a free PCR test as normal by calling 119 or visiting gov.uk/get-coronavirus-test, and should be reassured that these will be processed at other NHS Test and Trace laboratories around the country."
The UK conducts hundreds of thousands of PCR tests a day, with 435,682 carried out on Wednesday, according to the latest government figures.
But some members of the public have now been urged to book further testing. West Berkshire Council said in a statement some of the tests at the Newbury Showground testing site, operated by the Department for Health and Social Care (DHSC), "have had results sent out that may have incorrectly shown as negative for Covid-19".
"After receiving reports from local residents in recent weeks that there were concerns about the accuracy of test results from the site, we passed these concerns onto the DHSC for further investigation," the statement added.
"The Department of Health and Social Care (DHSC) has now confirmed that a number of sites nationally may have been affected by this issue, including the one at Newbury Showground."
Those who received a negative result for a PCR test between October 3 and 12, as well as their close contacts, were "strongly" encouraged by the local authority to take another test.
Councillor Graham Bridgman said: "Testing continues to remain important as we learn to live with Covid and anyone who has symptoms, or who has been in contact with someone who tests positive, should book a PCR test straightaway. We also strongly encourage the public to do twice weekly lateral flow testing."
It comes as fully vaccinated people arriving in England from countries not on the red list have been told they can take a cheaper and quicker lateral flow test rather than the PCR version from October 24.