Video report by ITV News Correspondent Lucy Watson
Delays to British Airways flights are likely to continue into Thursday, despite the IT glitch which caused more than 100 flights to be cancelled and 200 to be delayed being fixed.
The airline said "flights were returning to normal" but warned there "may be some knock-on operational disruption as a result of the issue earlier."
Tens of thousands of holidaymakers at Heathrow, Gatwick and London City airports were affected by the delay on Wednesday.
BA cancelled 117 flights at Heathrow, while 10 were axed at Gatwick.
Passengers shared images of long queues at the airports, along with error messages showing on the BA app - some services which were not cancelled were running five hours behind schedule.
The failures affected short-haul flights at the UK airports and customers were told to allow extra time at airports.
In a statement, BA apologised to all customers for the disruption, but the airline could face a compensation bill in excess of £8 million if all those affected claim what they are entitled to under European Union rules.
The airline was forced to use back-up and manual systems to try and cope with the issues.
"We apologise to all our customers caught up in the disruption, and appreciate how frustrating their experience has been," BA said.
"Our teams have been working tirelessly to get the vast majority of customers on their way, with most of our flights departing.
"Our flights are returning to normal, however there may be some knock-on operational disruption as a result of the issue earlier.
"We continue to advise customers to check ba.com for the latest flight information before coming to the airport."
The company said customers on short-haul services leaving from Heathrow, Gatwick and London City would be allowed to rebook flights for another day.
Holidaymakers even struggled to get to Gatwick Airport after the Gatwick Express train service from London Victoria was cancelled, following a fire on the tracks between Victoria and Clapham Junction.
Kevin Archbold was stuck at Heathrow Airport for several hours, after his flight to Zagreb, Croatia was cancelled.
He told ITV News he queued up for BA customer services for half an hour, but found out his flight has been scrapped by calling up the airline.
"There was no communication from British Airways," he said. "I drove here this morning, until I know I can't be re-booked onto another flight, I won't go home.
"I am sat in Heathrow waiting for the system to be rebooted.
"The customer service has been absolutely shocking, I will not be flying with BA again, I am going to fly with budget airlines now.
"At the end of August, I am flying to Las Vegas with BA, but I am terrified something will go wrong."
Darren Rowe, from the Cotswolds, said his 10.20am flight to Hamburg from Heathrow for business meetings was cancelled before "all chaos let loose".
He said: "There were massive queues, it was queue here, queue there, nobody was saying anything. The lack of information was just pathetic.
"You've got young families in that queue, people going to weddings, birthdays, on business. They could have had somebody come around with water updating people about what was going on."
BA is offering passengers departing from Heathrow, Gatwick and London City the chance to re-book to another day between Thursday and next Tuesday.
Passengers took to social media to voice their frustration at the delays, with some people claiming they were stuck for hours.
One passenger wrote: "Taken us an hour to check in at Gatwick this morning with british airways now on my flight to be told we can’t take off due to a system failure."
Another wrote: "Been on the tarmac 3 hours in Lyon, France bc of @British_Airways computer glitch. If we get in the air, really, really hope we make our connection London to Austin."
"Major computer failure with British Airways at Gatwick this morning," David Hewson wrote.
"This is the queue for the queue at check-in. Currently stuck on ground cos pilot can't get data. Set off early if you have a flight."
BA's problems come after it suffered a major computer failure over the spring bank holiday weekend in May 2017, stranding tens of thousands of passengers and costing owner AIG around £80 million.
On that occasion, the airline cancelled 726 flights due to a power failure, sparking a raft of compensation claims for flight costs, train and hotel expenses, replacement clothes and toiletries.