It sounds like the UK hunters are not so unlike US hunters of yesteryear. Nowadays, most states require some hunter safety training and allow for some "grandfathering" of older hunters that had licenses before the training requirements.

While it's not common, there are hunting accidents in the US reported by the media, seemingly every year. However, given the sheer quantity of hunters, I believe the stats would reveal very low % of accidents. I suspect not a lot of difference between UK and US in hunting accidents per hunter.