There are long inquiries and court cases in the US as well. Jury of peers, the whole lot. I'm not sure how the 'balance is about right and nothing like the USA'. When called upon in a moment of crisis, these people got onto a train and shot an innocent person in the the head half a dozen times, from close range.
The big difference is, there are fewer opportunities for armed police to screw this up. There are far fewer of them (heavily armed police are the exception, rather than the default) and they are not nearly needed as often (the citizenry is not as heavily armed). The policy that largely prevents the mistakes is what really helps, rather than having better armed police or better post-cockup inquiries (both of which, to me, seem fairly debatable).
The big difference is, there are fewer opportunities for armed police to screw this up. There are far fewer of them (heavily armed police are the exception, rather than the default) and they are not nearly needed as often (the citizenry is not as heavily armed). The policy that largely prevents the mistakes is what really helps, rather than having better armed police or better post-cockup inquiries (both of which, to me, seem fairly debatable).