Complaints procedures in universities are in a mess. Internal mechanisms for dealing with complaints are being improved now. But external mechanisms are often archaic, confusing and unfair. If you ask what the system is for external complaints, there are two answers. Older universities set up under royal charter are bound by decisions of the visitor, an external and arguably independent person whose authority on dispute resolution is upheld by the courts.
New universities are subject to judicial review separately through the courts.
Historical accident and a certain arrogance by some universities that the system was working and didn't need changing. It wasn't and it does. They include the Queen and various other royals, the archbishops of Canterbury and York and a selection of lords and earls. But don't expect a visit from the Queen if you want to complain about your supervision. These cases will be dealt with by the Privy Council Office or the Lord Chancellor's Department in Whitehall.