The UK Competition and Markets Authority has opened "enforcement cases" against two of the country's biggest airlines.
British Airways and Ryanair were already under investigation by the CMA for refusing to give refunds to people who were unable to fly during the UK's coronavirus lockdowns.
The body has now decided to go a step further and has asked the airlines to respond to its concerns.
Andrea Coscelli, chief executive of the CMA, said: "While we understand that airlines have had a tough time during the pandemic, people should not be left unfairly out of pocket for following the law.
"Customers booked these flights in good faith and were legally unable to take them due to circumstances entirely outside of their control. We believe these people should have been offered their money back."
The issue centres around flights that were not cancelled but which passengers could not legally board due to the UK's lockdowns and travel restrictions. BA and Ryanair only offered customers vouchers or the option to rebook their flights for a later date, rather than a cash refund.
The CMA did note that Ryanair "repaid a small number of people having reviewed the specifics of their cases".
A British Airways spokesperson told Bristol Live: "During this unprecedented crisis we have issued well over 3 million refunds and helped millions of our customers change their travel dates or destinations and we're grateful to them for their ongoing support. We continue to offer highly flexible booking policies at the same time as operating a vastly reduced schedule due to Government-imposed travel restrictions, and we have acted lawfully at all times.
"It is incredible that the Government is seeking to punish further an industry that is on its knees, after prohibiting airlines from meaningful flying for well over a year now. Any action taken against our industry will only serve to destabilise it, with potential consequences for jobs, business, connectivity and the UK economy."
Ryanair, meanwhile, said: "Ryanair today (9 June) welcomed the UK CMA's update on its review of airline policies on refund requests made by UK consumers whose flights operated during periods of lockdown.
"Ryanair has approached such refund requests on a case by case basis and has paid refunds in justified cases. Since June 2020, all our customers have also had the ability to rebook their flights without paying a change fee and millions of our UK customers have availed of this option."
