In a system of government founded on a Constitution, those laws have to follow the Constitution (at least in an eventually-consistent way). (Or the Constitution must be amended, or a revolution has to happen; neither of the latter two are possible by a legislature acting alone.)
You don't need a constitution for this purpose, even though a constitution can have practical benefit. And furthermore, you'd only be passing the buck by appealing to a constitution. I could just ask whether the constitution is arbitrary, and in this case, you could not appeal to anything to ground or constrain it. The ultimate ground for the written law is the moral law, such that the first is a determination of the second given the circumstances of a given jurisdiction. Note also the distinction between lex and ius.
It’s not that you need a constitution, but rather than many democratic governments have a constitution and that must be considered in the context of “when you're making new laws you can make those laws say anything you want”.
