British Airways said it is planning to run a "near normal schedule" at Gatwick today, and the majority of Heathrow services, after a global IT meltdown caused bank holiday weekend chaos.
It has though, warned there will still be "some knock-on disruption" to its schedule, as both aircraft and crews are out of position around the world.
Major problems with BA's systems led to disruption for thousands of passengers as all flights from Heathrow and Gatwick were cancelled yesterday.
Earlier on, the airline said most long-haul flights due to land in London were expected to arrive as normal.
The airline has apologised for the disruption and said it is refunding and rebooking affected customers.
It has asked people not to come to the airport unless they have a confirmed booking for travel. BA has also advised customers to continue to check the status of their flight on its site www.ba.com before heading off to the airport.
Gatwick has also told customers to keep checking their flight's status before travelling to the airport.
The airline said there was no evidence the IT issues were the result of a cyber attack, with BA chief executive Alex Cruz saying he believed the "root cause" was a power supply issue.
The crash in the computer system used to keep track of passengers left the airline unable to allow people to board flights. It also affected the airline's call centre and website, making bookings impossible.
Passengers reported massive queues at Heathrow, with others saying on social media that their plane was stuck on the runway for more than an hour.
As well as a bank holiday weekend in the UK, the timing also coincides with the start of the half-term holiday for many people.
Other airlines flying in and out of the London airports were unaffected.