Some major legal codes in the world right now include Common Law and Civil Law.
Common Law is the most often portrayed in media because it is the law system of the United States, Canada, the United Kingdom and a good chunk of the world (about 2.25 Billion People) live in a Common Law (or mostly common law... Scotland is weird, Quebec and Louisiana have some elements of French derived Civil Law, Isreal and India use religious laws/nation of origin laws in family and personal law (i.e. Marriage).
The Hallmarks of a Common Law system include the concept of Stare Decisis (latin, roughly means "the decision must stand"). This means that if a court in a common law system has two very similar cases, the court must decide in the same way for both outcomes as must all lower courts below that court. In addition, common law allows courts to see precedence in other jurisdictions and use them in deciding cases. The bulk of modern negligence law in nearly all common law countries comes from courts in Scotland, not local legislation. This isn't always the case, though. For example, in the United States, if a law contradicts the constitution, than the common law decision isn't good. It also makes it that some laws are never quite "statutory" or written down. England only recently got a "statutory" murder law on it's books. Prior to that, murder was a common law offense. Similarly, Michigan did not have a "statutory murder law" until the 1990s when it suddenly became important and Maryland does not have Statutory Murder to this day.
This is likely a boon to your kingdom as Common Law does not have a codified book of rules that you can read... but years of "we decided this long ago".
Another feature is the Jury Trial. In law, there are two elements called "Trier of Law" and "Trier of Fact". The Trier of Law is the person who answers the question "Is this illegal" and in Common Law, it's normally a Judge. The Trier of Fact is the person who answers "Did the illegal act occur?" and that is a Jury.
The big difference in Civil Law (and it's predecessor, Roman Law) is that Judgements do not set precedence for future judgements (but may be used persuasively) and that the court is Inquisitorial (as opposed to Adversarial, in the Jury Trial system). This means that the judge is both Trier of Law and Trier of Fact, and may thus ask questions of the witnesses. Civil Law also uses Statutory Laws, which means each crime is written down somewhere and the sentencing is prescribed with the law. Sentencing is also part of the trial phase in Civil Law, so mitigating factors (and aggravating factors) play an important part in the this part of the trial, where they have no bearing in a Common Law trial (you are sentenced after you're found guilty). This is why "We were just following orders" was thought by the Germans at Numberg to be an effective defense. In German Civil Law, having no personal motivation in your crime (such as you did it because it was your job and not because you had a personal ill will to the victim) was a very mitigating factor. Because Numberg used Common Law (because U.S. and UK could get behind Common Law, where as French Civil and Soviet Civil Law were not quite compatible). The problem the Germans faced was that Common Law first determines that the crime happened, then determines the degree of guilt.
Most of Mainland Europe and non-England European Colonies use Civil Law. The only other legal systems I can offer are Sharia Law... and that's all I'll say on that... Catholic Cannon Law (which is all but extinct, it's only used for some elements of criminal code in Vatican City, but they are more likely to use Italian Law).
Japanese Law from the late 1800s onward is some form of Civil Law (much of Japanese government as a whole are borrowed from European systems that worked. They have German Diet parliment, U.S. Constitution, British Post, French Civil Law, but with American Plea Bargaining). Prior to that, it was largely based on law dictated by Feudal Lords. They largely adopted Civil Law in the Meiji Restoration because it closely resembled their own Feudal systems. Recently, they also adopted "Citizen Judges" which is sort of a Jury system. Three Judges are career judges while the rest (up to seven, I think... it varies on crime) are similar to a United States Jury. The difference here is that Simple Majority is needed for Not Guilty while a Guilty verdict needs a Simple Majority and must include at least one career Judge in that vote.
Hope this was helpful. Law systems are a hobby of mine, so feel free to ask questions.
Edit: Related to statutes there is a significant difference in how they are written in Common Law and Civil Law. Because of Stare Decisis, rulings on a particular law are effectively an addition to that law. This means that from the legislative side of the house, a new law doesn't have to be a tome covering every possible scenario. For example, in most of the rest of the world, Anti-Trust laws are massively complex. In the United States, the Sherman Anti-Trust act was originally passed with three sentences. The scope of what is the law is still quite large, but that entirely originates from case law AND a few legislation acts to fix what some case law broke. As discussed earlier, several common law jurisdictions didn't have any statute against murder (though they did have sentencing guide lines) until relatively recently.
Conversly, as stated in a comment, Civil Law can review established case law as a sort of guideline, but isn't obligated to rule the same way in a similar case UNLESS the legislature has codified the ruling into an actual law. Thus, they tend to have numerous statutes that are long reads covering as many possible questions as they can think of.
Another final topic on Common Law: While this is not true of all jurisdictions, many common law systems require that there be an actual real case, and not a hypothetical. If, for example, in the United States I sue the government for failure to recognize that Vampires have rights under the constitution, I must be a Vampire to make my case. The fact that I am not would immediately get the case thrown out of court because I have no stake in vampires rights (Pun intended... it helps hammer home the point.).