Any citizen may exercise their right of access to law, and this includes the right to bring about a Private Prosecution. This right is honoured throughout the UK *
Obvious examples might include Statutory offences which led the citizen to suffer a loss (e.g. a Theft; a Fraud, the breach of a Copyright prohibition) and offences in Tort (e.g. a Nuisance; Defamation). Less obvious examples are offences which have not put the individual at a loss (e.g. a hazard which may put others at risk, to which the remedy may be an injunction) or, and I guess this illustrates whatever it is that is troubling you, a Byelaw which regulates the activities on private land. Some of these prosecutions might be matters which the state could have prosecuted. Some might involve a significant loss to the aggrieved party which might otherwise have been the basis of a Civil Claim but where the Criminal Prosecution provides a more appropriate remedy or a better established standard of evidence.
I have attended several Private Prosecutions, and while the Courts sometimes appear clumsy in managing these cases, they are generally very willing to hear them. There are some Judges who regularly hear Private Prosecutions for defamation or libel, notably Mr Justice Tugendhat (and I find nothing 'clumsy' in his Judgements!). It might interest you to look at the guidance published by the Crown Prosecution Service (CPS) to clarify whether or not the organisation should intervene in a Private Prosecution, and how it should make that decision.
High-profile Private Prosecutions in recent times include the successfull prosecution by the British Phonographic Industry (BPI), a trade body for the music industry, against the Cowan family and associates in Co.Durham for conspiracy to defraud, tax evasion and benefit fraud, following an extensive CD and DVD counterfeiting operation; and several prosecutions by the Royal Society for the Prevention of Cruelty to Animals (RSPCA) for violent acts against animals; both resulting in custodial sentences.
Some high-profile Private Prosecutions were doomed to fail: you might recall that a Private Prosecution for neglect was attempted against the parents of missing child Madeleine McCann by an Andrew Bennett; and the parents of the late Stephen Lawrence began a Private Prosecution for the murder of their son.
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* Further notes:
1. Scottish Courts expect a high standard of evidence and a special interest on behalf of the Prosecutor, before listing a Private Prosecution (see Andrew Belch 1805). In contrast, the Courts of England Wales and Northern Ireland will not assess the merits of a case and will be very willing to hear the majority of claims, only refusing a limited range of matters (such as a claim of theft between husband and wife). There has been little appetite for Private Prosecutions in Northern Ireland.
2. A Private Prosecutor should be able to fund the full costs of the Defendant in the event of an aquittal. A Private Prosecutor pursuing a Criminal matter may apply to have their costs met from central funds.