Hundreds of thousands of passengers were caught up in the disruption after flights were cancelled following a Nats technical issue on Tuesday.
Flight disruption that caused chaos for hundreds of thousands of passengers is expected to ease on Thursday.
Technical issues with air traffic control systems have caused more than 2,000 flights arriving or departing the UK to be cancelled since Tuesday.
The disruption is expected to lessen on Thursday and flight schedules return to normal, although Martin Rolfe, the chief executive of National Air Traffic Services (Nats), has faced calls to resign.
Among those calling for Mr Rolfe to step down has been Michael O’Leary, the outspoken boss of budget airline Ryanair.
On Wednesday, Mr O’Leary called Mr Rolfe’s position “untenable” and he is likely to issue further criticism when he hosts Ryanair’s annual general meeting at its headquarters close to Dublin airport later on Thursday.
Cancellations and delays continued on Wednesday as airlines dealt with knock-on impacts at airports including Heathrow, Gatwick, Manchester and Stansted.
It comes after the aviation analytics company Cirium said cancellations were slowing, with no flights cancelled for Thursday.
Some 2,145 flights were affected over the last two days, according to Cirium.
It said a total of 399 flights were cancelled or did not fly on Wednesday.
The worst affected airport was London Heathrow, which saw 79 out of a total of 666 departure flights affected.
Meanwhile, British Airways was the worst affected airline, as it saw 88 of its 507 flights scheduled to depart on Wednesday affected.
The airline said it was “incredibly sorry” to its customers and that the issue had been “entirely out of our control”.
The Civil Aviation Authority (CAA) on Wednesday said passengers are “unlikely to be entitled to compensation for delays or cancellations that were directly caused by the incident”.
A CAA spokesperson said: “We know many passengers have faced significant disruption and frustration following the Nats system issue on Tuesday September 8 and we understand the impact this has had on their travel plans.”
They added: “We consider that disruption caused by the Nats outage is likely to be considered the result of ‘extraordinary circumstances’ under passenger rights rules.
“This means that although passengers should be looked after by airlines, they are unlikely to be entitled to compensation for delays or cancellations that were directly caused by the incident.”
Transport Secretary Heidi Alexander told MPs on Wednesday afternoon that she did not believe the air traffic control issue was “unavoidable”.
Addressing the Commons, she said: “A four-hour air traffic outage yesterday left hundreds of thousands of passengers facing cancellations, diversions and delays.
“I would like to apologise wholeheartedly to passengers for this disruption.
“We often take for granted the way in which our aviation system just works, but yesterday that was not the case.
“Safety must remain air traffic controllers’ overriding priority, and this morning I have spoken to Nats chief executive Martin Rolfe, who informed me this outage was due to a technical issue at their Swanwick site.
“So, while my understanding from Nats is that we can rule out a cyber attack on this occasion, I do not believe this issue was unavoidable.
“We also spoke this morning about how Nats responded to resolve and minimise the disruption as quickly as possible, and I am grateful to the airports and airlines who responded straight away.”
Ms Alexander said she had asked the CAA to conduct an independent review into the incident, which is due to report to her within six months.
Nats also said a full investigation will be conducted into the issue.
The air traffic services provider has apologised for disruption to passengers and airlines, for which Mr Rolfe said he took “full responsibility”.
BA said it has “long made the case for improved resilience in aviation” and issues raised by the system failure need “to be addressed as a matter of urgency”.
A BA spokesperson said: “We’ve heard reassurances before, but then we’re faced with issues like this yet again.
“Our customers and colleagues are tired of dealing with these issues, time after time. This needs to be addressed as a matter of urgency.”
On Wednesday, Downing Street said the Government still had confidence in Mr Rolfe.
