I'm assuming that the idea of this question is "what happens if the British shoot down or sink a civilian transport belonging to some neutral country", not necessarily a Brazilian airliner.
Ignoring for the moment any questions about how it happens, I can't see it changing very much. The British aren't going to hunt it down in Brazil or Chile, it would have to be pretty close to the combat zone to be targeted even accidentally. Under those circumstances, I suspect that there would be a muted expression of regret by the British government and some sort of compensation would be awarded, but the general attitude would be that sometimes in a warzone, accidents happen. It's hardly a PR disaster because I suspect most people would think that anyone who goes swanning around a combat zone in that fashion is deliberately taking the risk - the people who made the decision to go in there without being assured of safe conduct have to bear some of the responsibility for what happened.
If the civilian vessel/aircraft is genuinely lost, then as others have pointed out it is massively off-course. Once again, it would be regrettable if it were attacked but the British (or the Argentinians, for that matter) would arguably be within their rights to engage anyone in the area who didn't positively identify themselves as friendly or non-combatant.