The UK had this problem with the Royal Ulster Constabulary, and more generally the policing of Northern Ireland with troops. The only way out of it was the restructuring, renaming, and re-populating with affirmative action of the force as the Police Service of Northern Ireland.
Another key part of the solution is a willingness to actually prosecute unlawful shootings. The key case here is Lee Clegg, a paratrooper on a roadside checkpoint who shot at a car driven by teenage joyriders that failed to stop. It was ruled that shooting after the car had passed was no longer justified.
The US has got to this point because it is not willing to effectively prosecute the use of lethal force against black men where it is not absolutely required. The US also has a very flexible and expansive idea of "required".
(PSNI are routinely armed, unlike most of the rest of the UK, except anti-terrorist patrols at airports and high security locations.)