If you want to guarantee that an airline won't ask you for the credit card used to pay, then don't book directly on the airline's website.
You can happily book on BA.com. You should always - always - tick the box to say the cardholder isn't travelling when you enter the payment details to ensure that you aren't asked for the card when checking in, and don't need to worry about what happens if your card is lost or replaced in the meantime.