Basically the police can stop you if they have "reasonable suspicion of committing crime x" and they have to tell you which crime they suspect you of and why.

Basically the police can stop you if they have "reasonable suspicion of committing crime x" and they have to tell you which crime they suspect you of and why. To prove who we are we can use a driving license or passport, if we have one. But there are many people with neither. In that case it's quite complex and usually requires a trustworthy person (doctor, lawyer, chartered engineer) who knows you well to confirm your identity.