Congratulations on your results! You definitely have a shot at the top-tier schools, though as always, nothing is guaranteed. Obviously you're going to be applying to some places like LSE and Oxbridge, and rightly so. Others can advise you on which you might want to select.
However, you'll also want to have a safety school, so that you know you'll be heading off to uni somewhere. Can I suggest Queen Mary, University of London, as a good option for that. It has a solid program, and a degree from there won't stop you from going anywhere (except the few blatantly Oxbridge firms/chambers that are still out there). It has excellent extracurriculars, including Pro Bono work and a Mooting team, and a number of very prominent authors are professors and lecturers there.
I'm not saying that it should necessarily be your first choice, but with AAA you're virtually guaranteed a place (assuming you've got a decent CV overall), and it's a nice place to be. Speaking from experience, there's a lot to be said for being a big fish in a small pond. As safety schools go, it's definitely not a bad one.