British Airways was expecting to run an almost full schedule from its London airports on Tuesday, after a failure of the airline's IT systems caused global flight disruption over the bank holiday weekend .
However, a "significant number of customers" remained without their luggage as a result of the chaos - and BA admitted it still had "work to do" reuniting bags with passengers.
Experts predict the knock-on effect of the IT outage could continue for several days and BA is facing huge compensation costs, with reports suggesting the bill could top £100m.
Speaking on Monday afternoon (May 29), Alex Cruz, British Airways chief executive, said: "At this stage we know there was an exceptional power surge that collapsed our IT systems, bringing down all our flight, baggage and customer communication systems.
"It appears to have been so strong that it rendered the back-up system ineffective.
"This resulted in an outage of all our systems across our 170 airports in 70 different countries.
"These systems are highly inter-dependent and normally transmit tens of millions of messages a day between different parts of the airline."
Mr Cruz continued: "At the moment, we do not have a complete picture of what happened.
"Our focus has been on putting things right for the customers affected.
"When that process is complete, we will hold an exhaustive investigation into the causes of this incident – and do whatever is necessary to ensure it cannot recur."
On Saturday night, travellers spent the night sleeping on yoga mats spread on terminal floors after BA cancelled all flights leaving the London hubs, while disruption continued into Sunday with dozens more services from Heathrow axed.
The IT outage had a knock-on effect on BA services around the world, while passengers who did get moving on the limited number of flights to take off from the UK reported arriving at their destinations without luggage.
The disruption also hit transport systems on the ground, with hundreds of travellers flooding London's King's Cross station in the hope of boarding a train north instead.
By Monday, services were back to normal at Gatwick while just under 10% of short-haul flights at Heathrow were still affected.
Keep up to date with the latest news in west London via the free getwestlondon app.
You can even set it to receive push notifications for all the breaking news in your area.