The Competition & Markets Authority (CMA) has opened a formal investigation following complaints a private firm, Expert Medicals, has not provided tests to travellers.
The government body also suspects the company does not return results in a timely manner or, indeed, at all.
Expert Medical is also accused of having failed to respond to customer complaints, as well as to issue refunds when due.
The firm, one of the largest providers of PCR travel tests in the UK this summer, has been the subject of a high number of complaints, both to Citizens Advice and more recently to the CMA.
It now no longer appears on the list of testing providers who self-declare that they meet the minimum standards for Covid-19 testing.
The CMA has also written to a further 19 test providers warning them to improve their pricing information or risk action in the future.
The body is concerned that the 19 firms continue to falsely advertise tests at very low prices when they are either not available at that price or include hidden conditions, such as where the tests must be collected from.
This action comes after the CMA last week sent an open letter to PCR test providers warning that a range of harmful practices in the sector could breach consumer protection law.
Andrea Coscelli, chief executive at the CMA, said: “Millions of people have to buy PCR tests in order to travel.
“If we find that firms have been misleading customers and failing to provide the service that people have paid for, we stand ready to take action.
“Our actions are the next steps in our work to ensure the PCR testing market works for consumers and we are preparing to take further action in this sector.”