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Ryanair boss Michael O'Leary has said Monday's failure of the UK's air traffic system was "not acceptable".
He said the airline had still not received an explanation as to what caused the problems and questioned why there was no back-up system in place.
In a statement on X, formerly known as Twitter, he said Ryanair had to cancel about 250 flights on Monday affecting 40,000 passengers.
However, he said services were expected to return to normal by Wednesday.
More than a quarter of all UK flights were axed on Monday after a fault with National Air Traffic Services (Nats), which runs air traffic control in the UK.
Delays and cancellations have been continuing on Tuesday, with Monday's disruption having led to some planes and air crew being stuck in the wrong location.
According to aviation data firm Cirium, 790 departing flights were cancelled on Monday, which it said was equivalent to about a quarter of all departures, and 785, or about 27%, of incoming flights.
Mr O'Leary said Ryanair had been in contact with Nats.
"We still haven't had an explanation from them on what exactly caused this failure yesterday and where were their back up systems," he said.
"It's not acceptable that UK Nats simply allow computer systems to be taken down and everybody's flights get cancelled and delayed."
Mr O'Leary said that about 20 Ryanair aircraft had not been able to return to their home bases on Monday.
He added that about 70 flights were set to be cancelled on Tuesday out of the 3,200 planned, and said the carrier was doing "everything we possible can to minimise the disruption for our passengers and their families".
Nats confirmed there was a problem with the air traffic control system shortly after midday on Monday.
It announced later it had identified and remedied the issue, but warned it would take "some time for flights to return to normal".
However, it declined to comment on what had caused the issue.
On Tuesday, it apologised again, adding: "Our systems are operating as normal and we are working with the airlines and airports to get people where they need to go and clear the backlog as quickly as possible."
It added that "a thorough investigation is now underway to understand the root cause of what happened".
The government has said that it has been told that Monday's problems were not the result of a cyber-attack.
The prime minister's official spokesperson said: "The exact cause of the technical incident will be subject to the investigation by the Civil Aviation Authority and then submitted to government."