While the issue had been “identified and remedied” by 3.15pm, the technical meltdown came during a busy public holiday and airlines warned there would likely be knock-on effects for days.
The four-hour outage has affected not only travellers plans but crew rotas and schedules.
British Airways has waived fees for passengers travelling with them on Monday and Tuesday to change flights, and warned travellers only to come to the airport if their travel is confirmed.
An apology issued from the Nats press office said they would be helping airlines get travellers back in the air.
“We are now working closely with airlines and airports to manage the flights affected as efficiently as possible. Our engineers will be carefully monitoring the system’s performance as we return to normal operations.
“Our priority is always to ensure that every flight in the UK remains safe and we are sincerely sorry for the disruption this is causing. Please contact your airline for information on how this may affect your flight.”
Heathrow International Airport, the UK’s largest port of departure for air travel, warned that “schedules still remain significantly disrupted”.
Aviation data firm Circum predicted 3049 departures would have been affected on Monday, and a further 3054 flights were scheduled to arrive.
As of 2.30pm local time, the BBC reported 503 fights had been cancelled, which it said was equivalent to 8 per cent of all departures, and 9 per cent of incoming flights.