It's the 15cm width which is problematic, very few people board a BA aircraft with their "hand bag" (second bag / personal item) within that dimension. However I did recently get this item


and it's quite tough and durable. It just about squeeze under a BA seat without being tipped flat, and obviously after take-off and before landing it can be placed directly in front of the seat so no legroom is lost at all, and it's well below the thighs.

Incidentally I got it because it is the one and only bag allowed on Norse for their base fares. So their £228 fares to New York gets you just this bag, to have a 10 kgs bag in the overhead locker costs an extra £37.