Hi there,
I'm working as an intern at Allen and Overy (one of the magic circle firms). All I can say is, NO - they don't care about your A Levels. They care about your undergraduate degree and your work experiences. A good degree is very important so make sure you put efforts in that. However, a lot of associates at the firm didn't graduate from top-notch university, they just have a decent amount of work experiences, so don't stress yourself too much.
Good luck!