For most lawyers and their clients, public law is about how public authorities make decisions. Is a decision procedurally unfair - has the decision maker, for example, taken into account some factor that is irrelevant, or ignored a point that is relevant? Are reasons required? Have they been given? Has the decision maker complied with all legal requirements in making the decision, including those imposed by EC law? Is the decision "irrational"?
You can go to the High Court and ask for "judicial review" of decisions which you claim are wrongly made. The court can order the decision maker to reconsider the claim, act in a particular way, or stop doing something. Judicial review is often the way forward in environmental cases.
Although it may seem a rather theoretical remedy, the aim is to cure the procedural flaw in such a way that there will be practical effects. Often the target in judicial review is central government - the relevant Secretary of State (often in our case of the Department of Communities and Local Government or of the Department for Transport). We also use it against local government, particularly planning authorities, and others acting under statutory powers, such as the utility companies and airports.
"Private" law is used in environmental cases when you are directly claiming against someone for causing a nuisance, causing you personal injury, trespassing on your land, etc. Familiarity with the environmental law and background science helps to win cases (and to judge which ones are not worth pursuing).