Point of clarification,
As D-man explained very well, the purpose of any act of self defense in to stop the threat.
While quite often a shot to the leg or arm might have the same effect in stopping a threat as a shot to the chest, the reality is that Police aren't trained to shoot center of mass purely because it's the mostly likely to stop the target when hit. When you are firing a projectile that will travel a high speeds until it hits something, you want to be damn sure it hits what you are aiming for and not go through a window half a block down. Simply put, the center of the body is the easiest (and most certain) target to aim for. Even if you miss dead center (the 10 point ring as it were), there is still a strong chance that you will hit the target.
Police in GB do manage to enforce the law just fine with limited access to lethal tools, but I don't think the environment they operate in is that similar to US cities. There have also been recent fatalities within the British constables due to being less armed than their adversaries.