British transport minister Mark Harper said it would take days to resolve the widespread disruption to flights into and out of the country after air traffic control systems were hit by a technical problem.
Over 1,500 flights were cancelled on Monday - one of the country's busiest travel days - after air traffic controllers were forced to switch to manual systems.
Harper added that government officials did not believe the technical problem was the result of a cyber attack.
"There is going to be some knock on impact today and I suspect for another few days as airlines get their planes and get their services back to normal," Harper told the BBC on Tuesday.
Aviation analytics firm Cirium said 790 flights departing UK airports were cancelled and 785 flights due to arrive were cancelled on Monday, meaning just over a quarter of all flights into or out of the country were affected.
Heathrow Airport, Britain's busiest hub, told passengers on X, formerly known as Twitter, to contact their airline before travelling to the airport on Tuesday.
Airlines said they were making changes to their schedules to try and fly as many people as possible but some planes and crews were not where they should have been.
"We're working as hard as possible to get affected customers on their way again," British Airways said on X.