Legal work experience is not required for entry into a law degree, including at "top" unis. In fact given the "top" law courses tend to be overwhelmingly academic courses, it's probably not even hugely relevant for them. They would be just as happy (perhaps more so) to see relevant wider reading and a critically analytical personal statement discussing that wider reading.
Note also outside of investment banking and management consulting, for "corporate" jobs (non-legal ones, at least) they don't care what uni you go to. So it's also a bit of a moot point for that anyway. You also don't need a law degree to do those non-legal roles and it's of no real benefit compared to anything else (you don't even technically need a law degree to become a corporate solicitor, I would note).