The airline said it planned to operate 60 percent of long-haul flights and 50 percent of short-haul flights from London's Heathrow Airport, allowing 70 percent of passengers to reach their destinations.
Flights from two other London airports, Gatwick and City, were not affected by the strike, which follows several others and is expected to last five days. A further two strikes are planned if the dispute cannot be resolved first.
British Airways Chief Executive Willie Walsh and leaders of the labour union Unite, which represents the cabin crew, blame each other for a breakdown in communication.
"I made an offer to Willie Walsh yesterday to put back our people's travel concessions that he's vindictively and foolishly taken away from them and I would personally call this strike off," Unite co-leader Tony Woodley told BBC Radio 4 on Monday.
The issue of travel allowances for cabin crew has become a major sticking point in the conflict, which comes at a difficult time for BA. The airline last week announced a record full-year loss of 531 million pounds ($763 million).
The latest round of face-to-face talks between managers and union leaders, on Saturday, came to an ill-tempered halt after protesters from a tiny left-wing political party invaded the venue.
It also emerged that Derek Simpson, joint leader of Unite, had been sending real-time updates to the microblogging site Twitter from inside the confidential talks, angering Walsh who appeared on television on Sunday to complain about it. (Reporting by Estelle Shirbon; editing by Tim Pearce)