Yes youre right. Blueonblue is describing a stop and search encounter and he is dead right in what he says about that but those are not the circumstances in which this man was being spoken to. It was as you describe, they were looking for a suspect for a crime and in the absence of any help from him as to whether he was that suspect they have a power of arrest in order to take him in and establish if he was that person or not. if not, he would be released. His charging for an offence, it was a public order matter, is not the offence that the original suspect was wanted for, because he was not the person wanted for that matter. Nobody other than the CPS lawyer will know why that charge of some public order offence was dropped.