I've had this several times with BA in South Africa, the first time I was asked in CPT and JNB when checking in both the outbound and return of an internal flight. On that trip I had left my usual card at home so each time it was an ID check and answer a couple of questions.

Since then I've always carried all my cards and have been checked 50% of the time. Multiple friends and family have the same checks. We have all been told it is due to the high prevalence of card fraud from those airports.

Not on BA but I have seen on Thai from LHR years ago someone denied boarding because they decided to do the card checks at the boarding gate and if you didn't have the card it was tough luck. As the woman was in front of me I heard the staff say if you don't read the rules it's not our problem.