As I understand it, the law in many US states on lawful self-defence is not dissimilar to that in England -- that is, you're allowed to use reasonable force to defend yourself against what you understand the threat to be at the time, even though your understanding may be mistaken, or even unreasonable.
This, combined with the requirement that the prosecution prove their case to the normal criminal standard by making the jury sure that the force used was unreasonable given the defendant's understanding of the circumstances (or that his understanding of the circumstances was not what he says it was), and the regular judicial advice to the jury, where appropriate, that they must remember the defendant was making a split second decision in highly charged and fast moving circumstances, generally makes it difficult to obtain a conviction, though the matter will generally come to trial if a police officer is involved simply because it's considered in the public interest to maintain confidence in the criminal justice system by letting a jury decide in police-related shootings.
The police in many US jurisdictions, though, appear to enjoy several additional protections from prosecution that are not available to the ordinary citizen, which is an area I just don't understand.
One big difference, of course, is that guns are far less widely available in the UK than in the US, so British police officers are far less likely to fear suspects will pull a gun on them, and because the police generally don't carry firearms, situations in which guns are involved, or likely to be involved, will normally be dealt with by specialist firearms officers who are trained in trying to subdue the suspect peacefully and whenever possible, only to use their weapons as a last resort.