An attempt to challenge a legal judgment which could potentially be worth billions of pounds to air passengers who have suffered flight delays has failed.

The Supreme Court refused applications by airlines Jet2 and Thomson to appeal against the Court of Appeal's decision in two cases about the airlines' liability to pay compensation after travel delays.

In the Jet2 case a passenger successfully challenged the airline's view that a 27-hour delay to an October 2011 flight amounted to an "extraordinary circumstance".

The upholding of the Thomson Airways case, which goes back to 2006, confirms consumers in England and Wales have six years to bring a claim for flight delay compensation.

Cheshire-based law firm Bott & Co said the Jet2 case could lead to claims of around £876 million a year from passengers while the Thomson case could lead to an estimated £3.89 billion in compensation.

"This is a landmark day for passengers everywhere," said David Bott, senior partner at Bott & Co.

Martin Lewis, creator and founder of MoneySavingExpert.com, said: "The clarity of this ruling is crucial for thousands frustrated by the airlines' stubborn attitude on this issue.

"Quite simply, the ruling states airlines are responsible for technical faults in all but extraordinary circumstances and that you can reclaim back at least six years."

Nathan Stower, the chief executive of the body representing UK airlines, the British Air Transport Association, said: "Today's Supreme Court decision is both surprising and disappointing.

"UK airlines support the principle of passenger protection and always meet their legal obligations. However, the rules should be clear, affordable and proportionate for the sake of passengers and airlines.

"The current system fails those tests and this decision will further increase costs which ultimately are borne by all passengers."

Andrew Haines, chief executive of the CAA, said: " We acknowledge airlines' concerns about the proportionality of the flight delay regulations and recognise that airfares may increase as a result. However, the court's decisions in these cases bring legal clarity to this issue and we now expect airlines to abide by them when considering claims."

"This is also important information for anyone who has made a claim for flight delay compensation but is waiting for a decision pending the outcome from the Supreme Court. Following the decisions in these two cases, airlines should not continue to put claims on hold. Where airlines have already put claims on hold, the CAA expects airlines to revisit them and pay compensation for any eligible claims.

"The CAA is not an ombudsman and does not have the power to force airlines to pay individual passengers' claims. If passengers do experience a long delay or cancellation and wish to claim for compensation, they should contact their airline directly."