Easyjet founder Sir Stelios Haji-Ioannou has threatened to take away Easyjet's right to its branding unless major improvements are made in its punctuality.
The entrepeneur sent a "cure notice" to the airline, asking it to reduce the number of flights that are cancelled, increase the percentage of its flights that depart on time, and ensure the average delay of its flights goes down.
The average delay of flights departing and arriving at UK airports in May was 26 minutes, a dramatic increase on the 9 minute average in May last year.
Easyjet said the poor punctuality figures were down to a number of factors, including crew and scheduling issues aggravated by air traffic control strikes.
The figures may also have been affected by the volcanic ash, and an increase in the number of routes the airline flies.
Sir Stelios has asked for the average delay each month to be reduced to less than 15 minutes by October 26, otherwise he will look at terminating the brand licence.
Sir Stelios said the number of customer complaints about Easyjet received by him had "increased significantly" and that the poor performance had the potential to "cause irredeemable harm to the reputation of the airline, the Easyjet brand and the Easy brand".
In an open letter to the chairman of the board, Sir Stelios set out his "frustration" at the "unacceptable operational state that the board has allowed Easyjet to reach".
"The result of the operational mess that the company is in is that it has too few staff to meet the number of flights it has sold," said Sir Stelios.
"This is extremely detrimental to the goodwill and reputation of the airline and the brand in particular. Many years of carefully building goodwill is being eroded in a matter of months.
"As the owner of this brand I cannot stand by and let this happen."
Easyjet said Easygroup has "no right" to terminate the brand licence.
"EasyJet is advised that the brand licence does not impose or create any contractual obligation regarding on time performance," said the airline in its interim management results.
An Easyjet spokeswoman told ABTN, however, that the airline recognised its punctuality and cancellation record has not been as good as it should have.
"We are looking into this but it is already clear that no single issue is to blame. It is a combination of air traffic control (ATC) strikes and go slows across Europe aggravating crewing and scheduling issues at some of our bases."
According to the airline, ATC industrial action this year has meant 48 days of disruption so far, compared to only eight in the whole of last year.
The Easyjet spokeswoman added: "We are also looking very closely at our schedules to make them as robust as possible going forward and have sub-chartered additional aircraft and crew to provide further cover."