Affected airports include Britain's largest hub Heathrow, as well as Stansted, Cardiff, Glasgow and Dublin in Ireland.
The National Air Traffic Control Service (NATS) said its Swanwick centre, in Hampshire, was having "difficulty switching from night time to daytime operation".
"Engineers are working to rectify the problem as soon as possible," said an NATS spokesperson.
"At night, when it's quiet, we can combine sectors of airspace. When it gets busy in the daytime we split the sectors out again. The voice communications system is configured to enable this to happen," a statement added.
Edinburgh, Manchester, Birmingham, Southampton, Luton, London City, Newcastle, Exeter, Bournemouth and other airports have also reported delays and are asking passengers to check with their airlines.
"Due to a technical issue with air traffic control, flights from many UK airports, including Heathrow, are subject to delay and cancellation," a Heathrow Airport spokesperson said.
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