How did you book the ticket? As in, did you use an online travel agent like Expedia, Orbitz, opodo? Or did you book it with BA's website or call center?

If you booked it directly with BA, there is a chance at check-in they may ask to swipe the credit card or do something else to verify the card used to purchase was an authorized purchase. Most times BA asks for no such things; but some of that may depend on the routes involved. When BA check-in in Europe has asked me for such card, it's always been for the first segment on the ticketed itinerary; sometimes I've not had the bank card charged and they still let me fly. But then again, I knew the card number info (and they could key it in if needed) and I have had elite status with AA and/or BA whenever this has been asked of me.

Most of my tickets flown on major carriers are purchased with bank cards not in my name. Problem for me are rare and have been dropping off in frequency. Some of the changes in outcome are due to airlines becoming more relaxed in parts about this than they used to be. I've never missed a flight because of this kind of situation, but some others have.