The only time I was in a situation like this was I was told that my father was going to pass away very soon and I needed to get to HEL on the next flight from LHR. BA offered a flex Y fare for £1,200 and AY for about £800; I went for the latter. In hindsight I've thought that I should have perhaps mentioned more about the circumstances when I called the airlines, but as I didn't, I'm not sure if bereavement fares are available...