Hi there,
I'm a die hard BA fan (well my Company switched their business travel to BA a couple of years ago) and so we have little choice. But when the service has gone wrong and I've moaned and moaned I have got a result out of them. You need to escalate your complaint and hit them with as many facts of the case as possible. I found it also helps to cc my letter to BA's Chief Executive.
I still rate BA and their crews are just about the best in the business but SIA, EK and CX run them very close.
Keep trying and don't give up on BA.