The economy section of the flight was full, and the cabin crew needed to move the woman and her grieving family out of that compartment to give them some privacy, the airline said.
The first-class passenger, Paul Trinder, told the Sunday Times newspaper that he was sleeping during a February flight from India and woke up when the crew placed the dead woman in an empty seat near him.
"I didn't have a clue what was going on. The stewards just plonked the body down without saying a thing. I remember looking at this frail, sparrow-like woman and thinking she was very ill," the newspaper quoted Trinder as saying. "When I asked what was going on, I was shocked to hear she was dead."
British Airways said in a statement that about 10 passengers die each year in flight and that while each situation is dealt with on an individual basis, safety is paramount.
"The deceased must not be placed in the galley or blocking aisles or exits, and there should be clear space around the deceased," the statement said. "The wishes of family or friends traveling with the deceased will always be considered, and account taken of the reactions of other passengers."
Because there was space in the first class cabin, that "allowed the family members traveling with the deceased some level of privacy in their grief," the airline said.
"We apologize to passengers in the first cabin who were distressed by the situation - our cabin crew were working in difficult circumstances and chose the option that they believed would cause the least disruption," the statement said.
David Learmount, a former pilot and cabin crew member who now writes about the aviation industry for Flight International magazine, said that each airline has to deal with the relatively rare situation on an individual basis. He said that diverting the flight would be an unusual move, and that the captain would be consulted before the crew acted.
"Personally, I think they did the thing that was the best thing to do," he said. "Really, you want as much as possible to isolate the person.
"It's an isolated incident. It's not as if it happens every day, but you do have to take in people's sensibilities when it does happen."
(Copyright Associated Press, All Rights Reserved.)