A technical problem with British air traffic control that caused major delays in UK and Irish airports today has been resolved after more than 200 flights were forced to cancel.
However, knock-on effects are expected to continue for the night.
People travelling this evening are being advised to contact the airport beforehand to check if their flight's departure time has been delayed.
Passengers are also being advised to carry essential items such as medication in their hand luggage.
Aer Lingus says one in 10 flights in and out of the country has been delayed, while Ryanair has also reported a significant number of delays.
Dublin, Shannon and Cork airports are all affected - but the situation across the water is significantly worse.
Up to 60 flights in and out of Heathrow Airport have been cancelled as a result of technical issues at the air-traffic control headquarters at Swanwick in Hampshire.
Delays have been building all morning for air travellers across the UK. Flights in the London area are worst affected, with cancellations to Geneva, Istanbul, Nice and at least seven other airports.
The service's night-time operating system, which combines sectors of airspace for when it is less busy, did not properly switch over to the daytime system, causing a communication problem with the centre's internal telephones. They stressed that safety was not at risk at any time.
Thousands of people were caught up in the chaos, which hit major airports including Heathrow, Stansted and Gatwick. Passengers are also expected to be affected as knock-on effects hit flights on Sunday.
Ryanair called for action to prevent it happening again. In a statement, the airline said: "Ryanair is calling on the Civil Aviation Authority to intervene and prevent further chaos for thousands of passengers affected by this ATC failure. While we acknowledge problems can occur, where is the contingency? It's simply not good enough and the CAA needs to act now."
The problem occurred when the 23 controllers on a night shift at Swanwick handed over to the 125 controllers on the day shift at about 6am.
Nats said that by 4pm they had handled 2,576 flights compared with the 2,905 flights that were dealt with at the same time last week, meaning that they were operating at about 88% of normal capacity.
In a statement, Nats said: "At night, when it's quiet, sectors of airspace are combined. As it gets busier in the daytime the sectors are split out again and additional control positions are opened to meet the traffic demand.
"Because of the problem with the internal telephone system, it was not possible to open the additional control positions this morning, resulting in a significant reduction in capacity in some areas of UK en-route airspace."
Heathrow Airport was the worst affected, with 228 cancellations - 112 in arrivals, and 116 departures, with most being short-haul flights. A spokesman for the airport said the cancellations represented 15% of their usual daily total of 1,300 flights going in and out of the airport.
Some passengers at the airport dozed on the floor while others lined up in long queues to rebook their flights, with customers reporting they had to wait for up to five hours to speak to a representative from their airline.
Gatwick Airport said "there may be delays to flights this evening" and urged travellers to check with their airline. The airport said there was spare capacity today however, which "allowed for flexibility and resilience within the schedule".
A spokesman for Stansted Airport said they had continued to experience delays throughout the day, which ranged in time from 10 minutes to four hours. The average delay was two hours, he said, adding that flights were expected to operate as normal tomorrow.
Many passengers expressed their anger on Twitter and spoke of "chaotic scenes" at airports.
Danny O'Donoghue, lead singer with The Script and a judge on BBC talent show The Voice, wrote: "Stranded @ the airport , anyone got any suggestions on passing time ...."
Twitter user @simonhartley wrote: "Darn NATS. Stuck in Madeira airport with at least five hour delay home so far :(."
And @MMorrissey wrote: "My flight to NY delayed but chaotic scenes here. In 20 yrs of business travel, never seen Heathrow in this state when there's no snow!!"
Eurocontrol, the European organisation for air navigation safety, said it had been working with Nats and its counterparts in Holland and France during the day.
It said about 1,300 flights, nearly 8% of all traffic in Europe, had been "severely delayed".
In a statement, Eurocontrol said: "This incident highlights once again the importance of the robustness of the technical systems supporting air traffic management and the need for contingency planning at network level to minimise the impact of any failures on the travelling public."
The Civil Aviation Authority (CAA) said: "The CAA is in close contact with Nats to ensure they are managing this operational issue effectively, and they are working to resolve the situation swiftly, while ensuring that the service remains safe at all times."
The authority said customers were entitled to assistance from their airline if they had been delayed for several hours, including being given food and drink, often provided in the form of vouchers.
For short-haul flights, passengers should receive help if the delay is more than two hours. That rises to three hours for medium-haul flights of 1,500km to 3,500km, or of longer than 1,500km within the EU. For long-haul flights, passengers should receive assistance once the delay is over three hours.
More than 100 Ryanair flights to and from the south of England have been affected, with 10 cancelled so far. The airline said: "We apologise to affected passengers, however these circumstances are entirely beyond our control."
A spokeswoman for British Airways said: "We are organising hotels for customers when appropriate. In addition, customers on cancelled services of course have the opportunity to claim a refund or rebook.
"We would like to apologise to our customers for the inconvenience caused.
"We are doing all we can to minimise disruption to our flights, but inevitably these issues have led to a significant number of short haul cancellations at some UK and European airports today."
Virgin Atlantic urged customers to check their flight status before leaving home, and thanked them for their patience.
EasyJet asked passengers to check in as normal but to use the flight tracker service on their website for updates. A statement on their website read: "Although outside of our control, we're sorry for any delays you experience today."