"Engineers are working to rectify the problem as soon as possible."
Travel expert Simon Calder said the problem was a "disaster" for travellers, while aviation analyst David Learmount aviation analyst David Learmount compared the issue to rebooting a personal computer.
"They've tried to bring some of the equipment online but not all is working satisfactory," he told Sky News.
"Unfortunately what happens after that is even if they get things back on right now there's going to be some delays for the remainder of the day."
The Stansted spokesman said: "There are restrictions on the air space and the flow of aircraft. Our first departures go at 6am, so that's when the problems started."
A spokeswoman for Gatwick Airport said: "There are some issues with the air traffic control system.
"The result of it is that, at the moment, 20 per cent of our flights are being delayed, by anything up to a couple of hours, but we're getting people moving and getting them away.
"There are no problems with arrivals at the moment."
Passengers are advised to check with their airline for the latest situation.
On its website, Ryanair apologised for any inconvenience, writing: "Ryanair has been advised of an equipment failure within UK air traffic control which will cause significant flight delays and possible cancellations."
Passanger Daisy McAndrew said she had been caught in the "unholy mess" at Gatwick as she tried to fly to Barcelona for work.
"As ever, staff have been fantastic but they know nothing other than the fact it is going to be a very, very long delay - very frustrating," Ms McAndrew told Sky News.
"And also, it's embarrassing, isn't it? When you look around a lot of people on my plane are not British, they are flying British Airways, they are probably trying to get back to Spain and they will inevitably be thinking this is something that could have possibly been prevented.
"It doesn't show our air traffic control system or our travel system in a good light.
"I have never heard of an example where every single plane is grounded - it's quite eerie when I look out of the window to see the tarmac in Gatwick, normally so busy, and also the sky above Gatwick which is normally busy - completely static, there's nothing moving."
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