Moving to LA from England to study fashion styling.Watch
You'll probably need to decide whether you want to get your degree from an art school - I'm sure prestigious places like SCAD (Savannah College of Art and Design), RISD (Rhode Island School of Design), and CalArts (California Institute of the Arts) probably offer fashion-related degrees - or do you want a traditional university like, for a random example, the University of Arizona or the University of Chicago.
If you are dead set on LA, however, one thing to take into account is whether you want to be right in LA itself as the Los Angeles metro area is huge. No idea they offer any fashion-related major, but for universities in LA itself, there's USC (University of Southern California), UCLA (University of California Los Angeles), Occidental, Loyola Marymount, and CSULA (California State University Los Angeles). If you're willing to be a bit further out but still in the greater Los Angeles area there's Chapman, Pepperdine, Whittier, the Claremont colleges (Pomona, Harvey Mudd, Scripps, Claremont McKenna, and Pitzer), CSU Long Beach, and CSU Dominguez Hills. Also CalTech, of course, but I'm guessing they don't offer fashion, haha. Getting further out you have places like UC Irvine, UC Santa Barbara, and more CSUs. I'm sure there's probably a bunch I'm missing but can't think of them off the top of my head.
So, yeah, plenty of unis in the greater LA area to have a look at. I don't know anything about art schools in southern California so hopefully someone else can chip in or you'll have to research them yourself.
Good luck! And remember, you can't use UK student loans at an international university so remember to consider cost!