For serious issues I would suggest writing a letter addressed to the CEO, forget e-mails. Several years ago, in 2010 to be exact, I had some service issues in regards to two flights in F to and from SFO, which also included a (failed) attempt by SFO BA staff to have me accept a downgrade to J by calling me four hours before departure while I was having lunch with a friend in Burlingame, not far from the airport.

When I was back in London I sent a letter to Willie Walsh written on Conqueror paper. In my experience physical letters are more likely to be noticed and answered than e-mails, even assuming that one happens to know the correct e-mail address. Three months later I got a lengthy e-mail as a way of apology from a senior Customer Relations manager that started as follows:

"Thank you for your letter addressed to Willie Walsh. He has asked me to respond to you directly on his behalf, and apologise for the length of time it has taken to respond.
I am extremely sorry your flight..."

You get the gist. I also got a bunch of mile credited to my BAEC account..