I've made 2 complaints to BA in my life. Both were sent by letter to BAEC.
On first occasion I had to send a chase-up letter before I received a response, but the response was detailed and acknowledged the points I'd raised.
Second occasion, as well as letter, I also sent an e-mail through the website. This was back in June this year and to date I'm still waiting for a response!

Personally I think this is appalling service and have indicated my thoughts when BA send me the service surveys to complete.
However, I did receive a response to letter (sent to WW) from the special team of assistants who deal with CS issues. This also had a telephone number which I called. Unfortunately, the verbal responses were like they were reading from a prepared script and I got the feeling there was no scope for anything that might not have been on the script!