The UK's National Air Traffic Services (NATS) said the technical fault was "identified and remedied" on Monday evening, but "significant disruptions" are set to continue over the next few days as airlines work to clear the flight backlog.
The technical problem was revealed at 12.15pm on Monday, causing staff to have to input flight plans manually until the automatic system was recovered at 3.15pm.
The network-wide outage caused the worst day of flight disruptions in the country since the eruptions of the Icelandic volcano Eyjafjallajökull in 2010. In total, 790 departures and 785 arrivals were cancelled on Monday, according to flight analytics company Cirium. The number is equivalent to around 27 per cent of planned flights to and from the UK.
"[The fault] was fixed earlier on this afternoon," said Juliet Kennedy, NATS operations director, on Monday evening. "However, it will take some time for flights to return to normal, and we will continue to work with the airlines and the airports to recover the situation.
"Our absolute priority is safety, and we will be investigating very thoroughly what happened today."
A day after the fault, several airports issued statements outlining the impact the backlog would have on Tuesday's flight schedule.
Heathrow has said its services will "remain significantly disrupted" and urged passengers to contact their airline before travelling to the airport. London Gatwick issued a similar warning, while London Stansted stated that "our terminal may be busier than anticipated". Luton Airport said that "flights may be subject to delay or cancellation".
As a result of the disruptions, many passengers earlier were stuck on planes on the tarmac waiting to take off, or being held in other countries' airport buildings while waiting for the fault to be fixed.
As of 9am on Tuesday, Cirium said 147 (5 per cent) of UK departing flights had been cancelled, as well as 134 (5 per cent) of arrivals.
The government said it is in contact with industry participants regarding the issue, with transport minister Mark Harper warning that it will take a few days to fully resolve the delays.
"The last time there was something this significant was about a decade ago, so these things do not happen frequently," he said. "It is going to take some days to get everybody back to where they should be."
British Airways apologised to affected passengers, saying: "Like all airlines using UK airspace, our flights have been severely disrupted … While NATS has now resolved the issue, it has created significant and unavoidable delays and cancellations. We're working as hard as possible to get customers whose flights have been affected on their way again and have apologised for the huge inconvenience caused."
The travel operator Tui warned its customers to expect "significant delays to some of our flights".
Oseloka Obiora, chief technology officer at RiverSafe, said: "Downtime in industries such as aviation causes incredible disruption, as we've seen by flights being grounded and major delays, so it is vital that organisations have observability to monitor their entire network environment. Having visibility over the condition of networks, infrastructure and applications based on data outputs can ensure that IT teams are able to better identify and resolve issues faster."
The Civil Aviation Authority (CAA) is said to be investigating the cause of the fault, but the government has said it is "clear it wasn't a cyber attack".
The government also advised passengers to read the CAA's guidance and be aware of their rights when flights are delayed or cancelled.
