We had 2 Comp A's whilst in the RAF, wife and I both lost our fathers during a tour in the US, with both trips on BA. They seemed to know the circumstances, and we were upgraded on one of the trips.
The Comp Cell were beyond reproach, advising us of the quickest route available and asking whether we wanted anything different. Met at London by cab and whisked to Norwich and Luton respectively, in time on both occasions I hasten to add.