It's not a requirement for studying law, however if you're thinking of becoming a solicitor or barrister I would always encourage it.
Work experience is a great way of experiencing a legal environment, finding areas of practice you enjoy and it's a great way of asking people about their experiences.
If you're interested in gaining some legal work experience, try contacting a local firm to ask for a couple of days. As you're 16 presumably, there may be limits on what you can do/see, but it's still a good chance to find out more about the career. You could also sit in the public gallery of your local magistrates or crown court to observe a trial. I personally found this to be a really interesting and accessible way of engaging with the legal sector.