I cross stitch regularly on international flights. The only time I've had something taken was my blunt nosed, child safe scissors at Narita (Japan) because the blades were a centimeter too long. The pendants with the cutter are listed on the "no" list for TSA, but short bladed scissors are usually okay.
I wonder if BA was thinking hypodermic versus sewing needle. I would go ahead and pack your hand sewing. The worst they can do is take the needle (you would not have to surrender the fabric). My needle got through security just fine in at Heathrow last month.
Cheers, K