British Airways haven't had a fatal since 1976
Presumably this accident to a subsidiary doesn't count?
22 August 1985; British Airtours 737-200; Flight 28M; Manchester Airport, England: The crew rejected the takeoff due to an uncontained engine failure. The failure led to a punctured fuel tank and a fire that spread to the cabin. The accident killed 53 of 131 passengers and two of six crew members.