Very serious complaints - you usually have to be dead for this to happen - get investigated by the Independent Police Complaints Commission.
To take one case, they are the people who took the police's word for it that Ian Tomlinson hadn't had contact with them, who believed the rush-job autopsy, who believed the cops that there weren't any CCTV cameras in the area of Tomlinson's assault until citizens went round and pointed out the many that were pointing directly at the area concerned.
"the IPCC - whose task is to independently investigate the police - was able to show that organisations including the Police Superintendents' Association, the Association of Chief Police Officers and the Police Federation were "satisfied" with the IPCC's performance; but it had no idea how the people making the complaints found its service. The IPCC concedes this is a "weakness", but it is much more: it reveals an organisation that has failed completely to be outward-facing and customer-serving. It is culturally tilted towards the police forces it is supposed to monitor, and financially incentivised to rely on their resources." http://www.guardian.co.uk/commentisfree/2009/apr/14/ipcc-ian-tomlinson-investigation