General Powers
Police have the same powers as ordinary citizens. They can ask people to stop and answer questions, accompany them to the police station or to hand over items. If a citizen consents (and that consent is freely given) there is no requirement for any special power. Special powers are required where a citizen refuses to comply with a police request. Without a special power the police would theoretically be liable to be prosecuted in the same way as anyone else who interferes with your person, liberty or property.
Special Powers
There are no special powers at common law that allow police to stop persons, demand identification or compel persons to be searched. See Rice v Connolly [1966] 2 All ER 649 per Lord Parker CJ: 'It seems to me quite clear that though every citizen has a moral duty or, if you like, a social duty to assist the police, there is no legal duty to that effect, and indeed the whole basis of common law is that right of the individual to refuse to answer questions put to him by persons in authority, and a refusal to accompany those in authority to any particular place, short, of course, of arrest.' As such, the government has legislated to assist police in their law enforcement role (which includes protecting citizens and investigating crimes) limiting rights of refusal in certain circumstances. However, if police act outside any special/general power the police officer's behaviour may be unlawful, evidence obtained as a result of the police conduct may be excluded or offences that have been allegedly committed against the police officer may not stand.