The decision followed an overnight breakdown in talks between the airline and the Transport & General Workers' Union over pay and sick leave, the airline said.
No new talks were planned as of Thursday afternoon.
The union -- representing 20,000 employees, including 11,000 flight attendants -- said it would strike Tuesday and Wednesday.
British Airways, Europe's third largest airline, said it would also cancel all domestic and European flights to and from London Gatwick. Overseas flights -- except to Tampa, Fla., Bermuda and Barbados -- will operate, the airline's Web site said.
Heathrow normally handles about 550 BA flights daily and Gatwick normally some 160 domestic and European.
Airline Chief Executive Willie Walsh reduced paid sick leave and the number of flight attendants on planes as part of a plan to save $98 million by 2008.
The last cabin crew walkout against British Airways took place in July 1997 over three days and cost the carrier $250 million.
Swim Week Miami Beach 2014 [PHOTOS]