If you're a student that qualifies as being from a disadvantaged background, you might want to look into organisations that organise work experiences for students. The SEO organisation and SMF (Social Mobility Foundation) are two such organisations that I know of and have worked with in the past and they do great work for students.
Other than that - open a directory and start emailing/writing to law firms in your area and hope for the best. CVs and cover letters are always worth sending out - you just need the one place to respond and any experience is useful as compared to a blank CV.
But realistically, you certainly don't need any legal experience until you're at university. No prospective law student's application is strenghtened by legal work experience since legal practice has absolutely nothing to do with a Law degree and legal academia. So don't worry about it at all.