G-BPED & F3G,
Don't confuse BA Miles with AirMiles. Although BA set up Airmiles, they are no longer associated.
I was caught by this following a Sainsburys promotion back in 2003, when you could convert their loyalty points into Airmiles. I did this at the end of their promotion, converting a fair ££worth of points into Airmiles. Only thing was their terminal didn't recognise my Airmiles account number, but the assistant spotted my Silver BA Executive Club card which at that time still had an Airmiles logo on it. Using the number from that card. the transaction went through and I thought no more of it .. until, fast forward 3 years, letter from BA to the effect that " your points are about to expire, purchase a full fare flight to retain them". Pointing out that these points had been "purchased" with a cash equivalent cut no ice and the points were lost.
Trivial, I know, but I have avoided BA ever since.