Supposing that there are natural laws, it might still be that there is no algorithm that can apply them in their entirety, if they depend on one or more undecidable problems. E.g., some people postulate that hypercomputation is physically possible, which by definition can't be expressed by an algorithm. But while the existence of such things can't be ruled out, I'd say we don't have any real evidence in favor of them.

Alternatively, the natural laws might simply contain an infinite amount of information, which could never be stuffed into a finite algorithm. E.g., if the ratio between the electron mass and one of the quark masses is an uncomputable real number. Or if there are infinitely many laws, governing deeper and deeper structure ad infinitum past the subatomic level. The latter has some philosophical arguments against it (why would we apparently be near the top of the infinite structure?), but the former is consistent with the apparent continuum that physical constants reside in.