The airline expects to send the last bags out in pursuit of their owners on Tuesday, in a minor public relations disaster for BA and the airport that has seen celebrity customers taking to social media to report their losses.
The problem arose in Heathrow's Terminal 5 baggage system, which previously caused mass flight cancellations for BA on the terminal's first day in operation in March 2008. While the glitch was resolved by Sunday and passengers can now check in bags as normal, BA said it could take several more days before all bags reached their owners.
The airline hopes to have dispatched the last bags from the backlog at the airport by the end of Tuesday – but was still advising its customers to now carry essential items on board in their hand baggage.
A Heathrow spokeswoman said: "We experienced intermittent issues with the T5 baggage system between June 26 and 29 which caused some bags to be processed manually. Passengers can now check in bags as normal.
"We are very sorry for the disruption passengers have experienced and we are working round the clock with airlines to reunite passengers with their bags as quickly as possible."
British Airways meanwhile said it had been working nonstop since the airport IT problems started. A spokesman said: "We are very sorry that this process is taking longer than anticipated, and we fully understand the frustration that this is causing.
"Although we have not been able to use Terminal 5's baggage system to its full capacity to manage delayed bags for the past four days, we have used a range of other methods to process bags and are hoping that the last remaining items will depart from Heathrow by the end of Tuesday.
"Given the nature of global travel and a range of complex security and customs regulations in some countries, it may take several more days to reunite bags with their owners."
Among the affected was one of India's most renowned musicians, Ustad Amjad Ali Khan, who was reunited on Tuesday with the lost sarod he has played for 45 years, which went missing when he flew back to Delhi on BA on Saturday. Coleen Rooney, the wife of footballer Wayne, claimed to have had four suitcases that eventually reached her in Las Vegas "ransacked".
The airline said customers would be compensated for reasonable expenses for essential items such as clothes, foods and toiletries on production of receipts.
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