Same thing happened to me when I were about 13, I got my first drill press, exactly same vice too and it was on brass, luckily the belt was loose. At the time I never knew about this problem with brass as schools used to give you a hand vice and give you a hole to drill, I always assumed it was ok as it's what I were taught at school, probably why they don't teach metal work in schools anymore.
Andrew- I used to machine plastic seals which couldn't be clamped most of the time and had to be held by hand, I used to use only slot drills as even the slow spiral drills were unusable. I admit I had many accidents on the miller at work, no emergency stop on machines either, it was a case of deal with it, this was the kind of place where you given an interlock key to over-ride CNC machine doors so you could catch the parts as they come off, one of the reasons I left.
Maybe someone should start a near miss thread,