All the criminal prosecutions must happen through the courts and the lowest level is district court level, after which they may be appealed to a higher court.
Regulatory matters usually start there as well, so any restrictions in a person's capacity to act, or their liberty will be run through a court.
However, and its a big "however", in planning matters the Planning and Development Act 2000 introduced Section 160, which allows members of the public to initiate legal action against people who are in breach of planning law.
This doesn't place the law into the hands of the public in a literal sense, but it allows members of the public to initiate actions that can result in fines or imprisonment or both.
IOW they don't have to wait for local authorities, who may be strapped for cash or manpower, to take legal action.
More powers like this for the public in company law and the laws governing the financial services sector would be a step towards genuine democracy IMO.