Aren't UK-style law systems kind of built upon precedents set by the interpretation of the law by judges? I don't like it either but that's how I've seen the differences explained
I am not a lawyer, but if I recall correctly there are three types of law : statute (what parliament legislates), common law (that which has built up over the centuries as "just the way we expect the law to work" and precedent ("this was unclear at one point but courts down the years have been convinced that what it means is x"). Appeals are usually on the basis that the court has misunderstood or misapplied the law and the outcome of these appeals form the precedents for future cases.
