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British Airways has said it will operate a full flight schedule from both Heathrow and Gatwick airports on Tuesday, the first time it has done so in days after a global IT crash caused hundreds of flights to be cancelled and delayed.
However, the airline admitted a "significant number of customers" are still without their luggage following the disruption which began on Saturday and affected 75,000 passengers.
On Monday night, BA posted an update on its website saying: "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.
"Although we have already flown many bags to the correct airport, there is still some work to do and 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 for holidays."
Earlier on Monday, BA's chief executive said the outsourcing of jobs was not to blame for a "catastrophic" IT failure.
Alex Cruz apologised "profusely" for the hardship caused to customers and insisted a similar incident would never happen again.
The Chief Executive of British Airways has apologised "profusely" to passengers who experienced "hardship" over the weekend as flights were cancelled after an IT glitch.
Alex Cruz denied the outsourcing of British Airways jobs was to blame for a "catastrophic" IT failure that brought the airline's operations to a halt.
He further offered assurances that no customer data or any list, including terror watch lists, had been compromised by the glitch.
Travellers face more cancellations at Heathrow on the third day of disruption since the IT glitch.
Display boards showed some flights cancelled, including planes to Copenhagen and Amsterdam.
The other cancellations were domestic flights to Glasgow, Aberdeen, Manchester, Leeds Bradford and Dublin.
While a number of weary-looking passengers filled the benches by departures, for the majority check-in seemed to be going smoothly.
British Airways passengers are facing a third day of travel chaos at Heathrow as the airline continues to deal with the aftermath of a global IT crash.
Both Heathrow and Gatwick airports have warned travellers to check the status of their flights before travelling to the airports.
BA said it will run a full schedule at Gatwick and intends to operate a full long-haul schedule and a "high proportion" of its short-haul programme on Monday.
The airline said it was continuing to make "good progress" in recovering from the worldwide IT glitch that grounded scores of planes, leaving thousands of passengers grounded.
Labour leader Jeremy Corbyn's election campaign trail plans have been affected by British Airways' flight disruption.
Mr Corbyn changed his original plans to fly to Glasgow due to ongoing flight delays and cancellation caused by theairline's IT system crash.
Instead he travelled north by train after an interview on ITV's Peston On Sunday programme.
It meant he had to cancel a planned afternoon campaign stop in the city but it said to be going ahead with a rally in the evening.
A Labour source said: "As a result of flight disruption Jeremy decided to travel by train to ensure he could be in Glasgow this evening."
British Airways passengers already facing delays after a computer glitch are also being hit with missing baggage issues.
One man caught up in the ordeal, which grounded scores of flights on Saturday, said the airline had lost his and dozens of other passengers' bags.
Terry Page said on arrival at Terminal 5 he and "about 50" others were told BA did not know where the bags were - and were hoping they would receive them on Monday.
"They said nothing," Mr Page claimed. "It's affected so many people.
"An 80-year-old lady was standing around waiting for announcements, et cetera - and she fell over.
"We helped her up and she said 'I'm just so tired'.
"There was a lady with her baby stranded, it was awful. It's been a terrible, terrible day."
Musician Charles Trippy, bassist with US rock band We The Kings, complained to BA via Twitter that his instrument was missing.
The band are on the bill at the Slam Dunk Music Festival, which has shows in Leeds on Sunday and Hatfield on Monday.
Trippy tweeted: "Dear @British_Airways please find my bass. It's getting frustrating that you don't know where it is. I kinda need it for work. No big deal".
Thousands of British Airways passengers left stranded after a global IT crash caused chaos are hoping to get on flights from Heathrow on Sunday.
The airline has said it plans to operate the "majority of services" from the airport after the IT meltdown led to flight cancellations at both Heathrow and Gatwick on Saturday.
Departure boards showed BA flights departing from Heathrow early on Sunday, but several flights were cancelled.
A Heathrow spokesman said "delays and cancellations of British Airways flights are expected".
The airport has advised passengers not to travel to the airport unless they have already rebooked their flights.
Latest ITV News reports
The chief of IAG, which owns BA, said airline boss Alex Cruz's team did "everything possible".
The airline says a 'power surge' was to blame for the disruption to its data system but electricity network tells ITV News that's "not so".