Betterfromabove - I know where you mean, so can appreciate the connection problems.
Nevertheless, unless you were on a fully flexible ticket, I don't think thateven if you had got through to BA, you would have had any better outcome. People who go on about the days when ground staff had the "discretion" to provide a different service, are talking about a different commercial world when airline fares were in real terms far more expensive,with far more fat to allow discretion. The walk up fares of £300 you ended up paying would have been closer to £600 in real terms when staff had that sort of discretion.
If you think BA are bad, I've recently had an experience with KLM where I had to cancel a Transatlantic non-flexible flight. No problem financially, because well-insured. However, KLM firstly denied any liability to refund taxes (but finally got them), and then I couldn't get any evidence from them that the sectors weren't flown for the insurance claim. Eventually I challenged the insurance company to do any better, but after 2 months they gave up as well and made a without prejudice payment. I hope that you have an easier time with BA !