The organisation found CCJs collectively worth more than £4.5 million have piled up against airlines including Ryanair, Tui and Wizz Air.
Wizz Air accounts for almost half the total amount, despite carrying fewer passengers than some of its rivals.
Which? said the "shocking scale" of these figures highlights how the enforcement of air passenger protections is "fundamentally flawed".
The government has outlined plans to enhance the Civil Aviation Authority’s (CAA) powers, but, according to Which?, "much-needed" aviation reforms have been delayed.
Wizz Air has 1,601 "outstanding" CCJs worth almost £2.2 million, according to the Registry Trust, which maintains the official statutory register of judgments, orders, and fines for England and Wales.
The register also shows easyJet has 884 "outstanding" CCJs, amounting to £611,436, and Ryanair has 840 worth £549,892. Tui has fewer, at, 313, but they are worth almost £1.3 million.
Trust Online, the official register of court judgments, told Which?: "Even when a judgment is paid, the judgment will continue to show as ’unsatisfied’ until the court records are updated."
It said defendants – the airlines in this case – are responsible for providing updates about the payment status of CCJs.
Jet2 has four "outstanding" judgments amounting to £1,434 and British Airways has 82 totalling £96,042.
As a result of the investigation, Which? has called for the government to prioritise giving the CAA the powers and resources it needs to directly fine airlines.
Rocio Concha, Which? director of policy and advocacy, said: "The scale of court judgments piling up against major airlines is a result of a system where the odds are stacked against passengers and airlines feel empowered to routinely ignore their legal obligations to pay out refunds and compensation.
"The CAA must get tough with airlines and make clear that it will consider using all the powers at its disposal – which may include reviewing the licences of the worst offenders if appropriate."
In response, Wizz Air said: "We pride ourselves on providing affordable, exciting travel opportunities and great service. We are sorry that, because of an unprecedented level of disruption due to the pandemic, we fell short of these expectations for some customers.
"We have learnt a lot from this challenging period and we are putting measures in place to ensure we are better prepared, including more customer services resources and revised processes.
"Since December, we have settled more than 400 CCJs. Regrettably there are outstanding cases that we are working to resolve as quickly as possible.
"In most cases, this is because we did not receive judgements from the courts due to problems receiving post, leaving us without the necessary information to settle cases.
"Online registers do not provide us with the information required to settle a case. We must, therefore, write to individual courts to apply for information about each case when we are made aware of it, and then wait to receive that information. This all makes for a complicated and time-consuming process.
“We are taking this matter extremely seriously, doing all we can to fix these issues and settle all outstanding cases as quickly as possible. Customers can contact us directly using our website or app to provide information about an outstanding judgment."
