BA is to resume all flights from today (Tuesday) after cancelling thousands of flights over the weekend.
The airline said its IT systems were back up and running and it would be operating a full flight schedule at Heathrow and Gatwick.
However, BA warned it could “take some time” to reunite travellers with their bags.
The cost of the IT glitch could reach £100 million in compensation with European Union compensation rules stating that individual payouts could be as much as £520.
But solicitors Bott&Co warn that the total cost could be as much as £150 million, as the firm says an extra £50m could be due for care and assistance including hotel accommodation for stranded passengers and additional expenses such as couriers for baggage.
All of its flights from Heathrow and Gatwick were grounded on Saturday and there were around 200 further cancellations from Heathrow on Sunday while many Gatwick flights were delayed.
Chief executive Alex Cruz said he was ‘profusely sorry’ for the IT meltdown which he put down to a power outage and failed back-up systems. He ruled out a cyber attack.
Passengers were affected at 170 airports across 70 countries.
Under European guidelines, all passengers flying from EU airports or flying into EU airports are entitled to claim compensation if their flight has been delayed by more than three hours. This varies from £220 for flights under 1,500km, such as London to Paris, to a maximum of £520 for delays of more than four hours to flights to destinations more than 3,500km away, such as London to New York.
These amounts are reduced by 50% if the airline is able to offer an alternative flight.
Passengers can apply for compensation through BA’s website, or through compensation claims firms.
BA has offered passengers affected by the glitch over the weekend a full refund or a chance to rebook and travel agents could face a flurry of calls from customers who booked through them.
The airline has also pledged to reunite customers with baggage via a courier free of charge and passengers are also advised to keep copies of receipts as they may be entitled to claim for some expenses.
BA says it will offer a full schedule of flights as of this morning (Tuesday).