British Bulldog is a violent game of 'it' with a somewhat complex set of rules. See the Wikipedia entry. We used to play it in the gym when it was too wet to play outside. Two boys were chosen as the 'bulldogs' and their role was to capture boys as they tried to run past from one end of the gym to the other (to stay in the game you had to go from one end of the gym to the other each round). The bulldogs territory was a line of mats lined across the middle of the gym, which you had to run over or climb past, hanging from the climbing frames each side of the gym.
If you were captured you became a bulldog, so as the game progressed, there were more and more bulldogs. The game was over when there were only two boys free. At that point a new round would start with the bulldogs coming from the winners of the previous round. Okay? Follow that?
The result was a lot of noise as boys ran from one side to another and a lot of violence. Violence was the reason why most schools banned the game so it is rarel played these days.
British Bulldog is played in the UK and in the old 'White Commonwealth'. However, very similar games are played in Germany and elsewhere in Europe with the name giving a clue to its origins. Wer hat Angst vorm Schwarzen Mann is the German name of the game, which losely translates as Who's afraid of the bogeyman? The origins of the game appear to be related to the Black Death, with the Black Death being 'it' and gradually building up in strength as the game goes on.
The picture is allegedly of British Bulldog but looks more like the more common game 'It'. What may make it British Bulldog is that the two boys in the centre appear to be playing the role of bulldogs but as it is outside and informal, no territory is marked out for either side.