The original duty of a Constable in England used to be to ensure that those summoned attended court and to keep the Kings' Peace. Enforcement of the law was the job of the courts and it was the role of the Coroner to decide if a crime had indeed been commited. The role of the police has been expanded and this is part of the problem. Except in the matter of public order (eg drunk and disorderly, or a brawl in public) the police should not have the authority to randomly pursue people they suspect of commiting a crime, or to arrest anyone without authority from the courts. Upon witnessing a potentual, or even actual, crime that is not a public order offence, the police should be required to report to the Coroner. The investigation of complaints and suspected crimes should be carried out by officers or the Coroners' department who have authority to search and to question, but not formally arrest If sufficient evidence of a crime is discovered, the Coroner could then issue a warrant and the Constabulary could act.
This takes away the 'right' of the police to arrest or otherwise interfere with people they don't like the look of. It takes criminal investigation out of the police culture, so that investigators do not learn the bad habits of uniformed colleagues. It should hopefully produce a higher quality of evidence as the result of a professional and unbiased investigation. More importantly, it places clear limits on the roles of the various agencies and will hopefully lead to recrutment processes that will place the right people in the right jobs.