British Airlines has now said it is aiming to operate a near normal schedule at Gatwick and the majority of services from Heathrow on Sunday.
Travellers tonight reported to the Sun Online that they have been able to check-in on Sunday flights, with it a flicker of hope for those left stranded.
It comes after angry travellers took to social media to complain about missed flights.
Huge queues formed inside and outside airport buildings today, one of the hottest days of the year so far in the UK.
Despite initial reports from passengers that the disruptions had been caused by a cyber attack, BA has said that a "power supply issue" was most likely behind the global IT failure.
Chief executive Alex Cruz said: "We believe the root cause was a power supply issue and we have no evidence of any cyber attack."
In a statement earlier today, BA said: "We have experienced a major IT system failure that is causing very severe disruption to our flight operations worldwide.
"The terminals at Heathrow and Gatwick have become extremely congested and we have cancelled all flights from Heathrow and Gatwick before 6pm UK time today, so please do not come to the airports."
The airline has since announced that flights from the two airports will be cancelled for the rest of the day.
They added: "We are extremely sorry for the inconvenience this is causing our customers and we are working to resolve the situation as quickly as possible."
There were reports of BA staff telling disgruntled passengers trying to get away for the Bank Holiday weekend that the company was under cyber attack.
Source: MENA
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