British police officers don't routinely carry guns and therefore couldn't possibly shoot you even if they wanted to. In fact, there is an almost zero probability of anyone in the UK getting shot by the police unless they happen to be committing an act of terrorism or murder at the time.
And of course https://en.wikipedia.org/wiki/Shooting_of_Jean_Charles_de_Me...
This is the disputed evidence at the center of the question; the gun was found several meters away from the scene, on the other side of a fence, "wrapped in a sock". There is a protracted argument about how plausible it is that he threw it there after being shot in the arm.
> they invariably seem to be about people who were in the process of attacking the police when they were shot.
If the police shoot someone, then of course all the official reports will say that they were attacking the police. There have been a number of mass casualty incidents in the UK (Hillsborough, Bloody Sunday) where the police or army reports turned out to be lies.