British Airways said it was resuming normal service on Tuesday but many customers are still without their luggage after three days of global flight disruption.
Some 75,000 passengers were affected by the computer system outage that caused chaotic scenes over a holiday weekend at London Gatwick and Heathrow, Europe's busiest airport.
"We are continuing to make good progress in reuniting bags with customers around the world who were affected by the major IT systems failure on Saturday," the airline said in a statement.
"We know there are still significant numbers of customers who are yet to receive their luggage.
"We are very sorry for the frustration this situation is causing at a very busy time of year," it said.
Speaking to Sky News television, BA chief executive Alex Cruz said "a power surge... had a catastrophic effect over some communications hardware which eventually affected all the messaging across our systems".
Some travellers slept at airports on Saturday and the disruption continued into Sunday with long queues at both Heathrow and Gatwick, while some short-haul flights from Heathrow were affected on Monday.
The computer crash had a knock-on effect on BA services around the world.
The GMB trade union blamed it on outsourcing of computer jobs to India last year.
But BA denied that this was the reason.
The company faces a compensation bill for accommodation and food of up to £100 million (115 million euros, $128 million).
On the London Stock Exchange, shares in the parent company of British Airways dropped 4.23 percent at the start of trading.