1. A loud gathering. It often refers to a tea party or other formal gathering. Primarily heard in UK. I hope that bun fight in the next room can contain themselves! They are being so noisy that we can't enjoy our tea in here!
2. An angry and/or impassioned exchange. A: "How long has this bun fight been going on?" B: "I don't know, it feels like they've been arguing for hours!"