I've never had any problems on BA, and in fact, found them quite good when I had to fly home for my dad's funeral.
I'm scared of flying and when dad passed away, I had to fly out on own because my husband couldn't travel at the same time as me (he followed several days later). We had to take a shuttle to board (climb up the steps( and when I was sitting there looking at the jumbo jet looming in front of me, I completely broke down. The flight attendants saw me and through my blubbering, I explained what happened AND that I was afraid of flying.
So they pulled me aside, gave me some water while the flight boarded (I was spilling it I was shaking so much) and they put me in business class. One of the flight attendants sat with me and held my hand during take off and landing, and they checked on me through the whole flight. I was embarrassed, but they were very nice and looked after me.
They were really good when it mattered the most.