The Court of Chancery and Equity is the foremost example of a central, non common law court. Although the Chancery was essentially an administrative department, it also played a judicial role. As a court of equity, it could try individual cases of hardship, where either common law provided no remedy, or the remedy had proved inadequate. The cases were wide and varied and concerned all those matters about which people could dispute, but which did not fall within the province of ecclesiastical law, criminal law, or the law of real estate.
In addition the King's Council, which in the reign of Edward I, consisted of thirty three men including the Chancellor of the Exchequer, the Justices of the two Benches, the Barons of the Exchequer, several itinerant justices and thirteen clerks of the Chancery, dealt with "petitions which were not thought appropriate for the chancellor alone to deal with." (22.)
The Other non common law courts included the Courts of Admiralty, which were established by Edward III in order to keep the king's peace on the high seas and to deal with piracy or "spoil' claims by or against foreign sovereigns, the Forest Court, whose records offer a commentary on the extent and organization of the royal forest, as well as the types of infractions committed against forest law, and the Court of Chivalry, which was concerned with the rights and responsibilities of the knighthood.
22. Baker, John H. An Introduction to English Legal History, 4th ed. London: Butterworths Lexis/Nexis, 2002 at p.117