I had a more positive experience of BA service recovery than the OP recently. Unfortunately I had reason to complain about the service in First on a LH flight (after numerous very positive experiences in F, this crew was really poor). Within 7 days of completing the on-line complaint form week my husband & I had both received an apologetic phone call from a member of the CS team who wanted to discuss our concerns in more detail. We were each offered 10,000 Avios by way of apology which we accepted. Maybe we were too easily pleased (as humble Silvers and long terms fans of BA) - but overall this felt like a satisfactory response.