Chaos at Heathrow caused by a strike by British Airways staff has begun to ease, but BA has warned it may take days to clear the passenger backlog.
Thousands of BA passengers have been stranded by the strike action
The airline will continue catch-up operations on Sunday, after over 80% of its scheduled flights ran on Saturday.
Up to 100,000 travellers are thought to have been disrupted by the BA strike in sympathy with sacked catering workers.
Talks between caterer Gate Gourmet and the Transport and General Workers Union (TGWU) will continue on Sunday.
Hundreds of BA ground staff went on strike on Thursday after Gate Gourmet, which supplies meals for BA flights, a day earlier sacked 670 staff.
Gate Gourmet said it had sacked the staff for staging an unofficial walkout over the firm's restructuring plans - this has been disputed by TGWU.
All-day talks between the company and union on Saturday, overseen by conciliation service Acas, broke up without resolution but will continue from 1100 BST (1000 GMT) on Sunday.
CHAOS AT HEATHROW
Wed: Gate Gourmet sack workers who miss a deadline to report to work. BA cancel four flights due to a lack of food
Thurs: Some BA staff stop work in sympathy with sacked staff. BA cancels all flights into and out of Heathrow
Fri: Talks begin between the union and Gate Gourmet. BA staff start returning to work.
By 2030 BST BA flights start leaving Heathrow
A Gate Gourmet spokesman said the talks had been "constructive", while the union said there had been "useful discussions".
Employees who had been sacked but were legitimately absent from work and did not strike on Wednesday were in the process of being reinstated, Gate Gourmet said in an earlier statement.
It is believed this involves 100 staff - Gate Gourmet had previously refused to hand back jobs to any of the staff. TGWU wants all 670 workers reinstated.
Millions in losses
The BA strike grounded flights for more than 24 hours - the cost to the airline in loss of revenues, refunds and the expense of accommodating passengers in hotels is estimated at up to £40m.
Services began operating again at 2030 BST (1930 GMT) on Friday.
The airline had hoped 85% of short-haul flights and 80% of long-haul flights would run as normal on Saturday.
Only passengers with reconfirmed reservations were asked to go to the airport.
Barriers have been in place in Terminal Four to prevent those without reservations being allowed through.
Some passengers have been waiting for flights since Thursday
BA marketing director Martin George told Sky News those who had been waiting for several days were not being given precedence over passengers with later bookings.
"We're working very hard on an individual basis to rebook them at a later time or on another airline, or offer them a refund."
Mr George said the airline was facing a massive logistical operation in order to recover from the strike, which had been "unofficial" and therefore harder to prepare for.
"When we started the operation we had about 1,000 flight and cabin crew out of position, about 100 aircraft out of position... that will take some days to recover," he said.
A BA spokeswoman said the airline also had about 30,000 bags to match with passengers.
"They are not with the people they should be with. We are working to return them," she said.
BAA, which manages Heathrow Airport, said it had contingency plans for passengers delayed at the airport.
Spokesman Mick Temple said: "We have experience of dealing with circumstances happening outside our control, such as 11 September."
Marquees had been set up with food and drinks for affected passengers.
During the holiday season, BA deals with 70,000 passengers at Heathrow daily.
AFFECTED AIRLINE NUMBERS
0800 727 800
0870 000 0123
Sri Lankan Airlines:
0208 538 2000
0870 850 9850
British Med Airlines:
0870 850 9850
Many disgruntled BA passengers blamed airport staff for poor communication and said the advice line for rebooking was constantly engaged.
BA said they had extra staff on duty and were trying to answer people's calls as quickly as possible.
Qantas, Sri Lankan, Finnair, GB and British Mediterranean airlines, also serviced by BA ground staff, were also affected.
Richard Wells, Gate Gourmet director, denied being heavy-handed over the sackings, insisting all those affected were spoken to and given written warnings before being dismissed.