I keep meaning to email The Magistrate to ask him if anyone's ever come before him to do so, but as a sort of continuation of the previous post I'll throw this out in general.
My own legal training, some years ago, was concentrated as you might expect on civil law; contract and tort chiefly. We passed through criminal law like someone skirting a disreputable neighbourhood, our Chancery barrister tutor raising a metaphorical nosegay to anything that strayed too far from equity and trusts.
But I paid attention to a lecture on magistrates, and in particular to the right of access of all persons directly to the court, to 'lay an information', or swear before a Justice of the Peace a criminal complaint against a named person. Magistrates could also issue arrest warrants from the bench, and accept charges. Thus it was then possible for a shopkeeper to arrest a shoplifter, march them down to the magistrate's court, lay an information and for the bench to charge the accused under the Theft Act, all without involving either the police or the CPS.
Though I can find a form on the Justice Ministry's website, I can't seem to find any cogent summary of whether these powers still pertain; your comments and advice are welcomed.