The chaos was made worse by a simultaneous computer failure at Maastricht in the Netherlands which covers airspace over much of north-western Europe.
At one stage, all commercial flights from British airports were grounded, causing long queues at check-ins.
A spokesman for National Air Traffic Services (Nats) said the disruption had been made worse by bad weather across Europe but added that the company hoped delays caused by the computer failure would be reduced to 10 minutes by the end of the day.
The disruption was caused by a glitch in an elderly computer at Nats centre in West Drayton in west London, which provides key information to controllers at the site and to their colleagues at Swanwick in Hampshire, Manchester and Prestwick in Scotland. An investigation was still under way into the causes of the problem.
The breakdown forced British Airways to cancel 22 services from Heathrow, where delays to other flights averaged an hour. Six services from Gatwick were cancelled and delays at regional airports were as long as two hours.
The computer at West Drayton near Heathrow went down at 9.30am for just 20 minutes, but the disruption came at a peak time of the year.
Hayden Evans, a controller at the new Swanwick centre and chairman of the Prospect union there, said: "It was quite a difficult situation. This is the busiest time of the year and people are working flat out.
"This was a major problem as far as controlling planes is concerned. It was a pretty massive achievement to get the system back to normal by 11am."
The computer at West Drayton produces flight progress strips for use by controllers. The pieces of cardboard show the last instructions given to pilots by overseas controllers before they fly into British airspace, including the flight number, call sign and height of the in-bound services. The British controller then assumes responsibility for the flight and issues further instructions.
Controllers' radar screens on which details of the flights appear remained functional throughout and controllers were able to speak to pilots and to controllers overseas to fill in the missing information.
That meant a substantial increase in workload and Nats decided to ground all flights preparing for take off at all the main British airports so that staff could deal with incoming aircraft and other planes already airborne.
A spokesman for Nats said about 80 per cent of capacity had been restored by 9.50am and full capacity was achieved by 11am. But disruption continued as staff struggled to deal with the backlog. No inbound flights had been affected, but short-haul aircraft preparing to take off for British destinations had been delayed.
In February, the same part of the system collapsed but the disruption was more limited because it was there were less flights operating.
Yesterday's mysterious computer failure also came just over a year after a bizarre electronic breakdown at the same West Drayton centre, which affected 200,000 passengers.
Meanwhile, leaders of the Transport and General Workers' Union are hopeful that talks can resume today over the dispute involving the catering firm Gate Gourmet. Stoppages as a result of the dispute caused the cancellation of hundreds of flights.