Something to keep in mind is that UC schools are required to set aside a certain number of places for California students, which means that students from other states and other countries are competing for a very small number of slots, that makes it much more competitive for them. Berkeley happens to be among the most competitive in the UC system. If you really want to be in California, you may want to consider private schools such as Stanford or USC. You are more likely to get individual attention for your application at these schools simply because they have fewer applicants and don't have to meet state quotas. In this case USC is a good choice because it accepts a very high number of international students and makes this a priority(sorry I graduated from USC and used to work in admissions, I'm biased). Courses will be smaller at these schools and because you are not a California resident the cost will be fairly similar. It is possible to get scholarships for studying in the US, but don't count on getting a scholarship from the Uni. Those scholarships are very competitive and often hinge on criteria that may be difficult for you to meet considering your international status. Instead try to find fellowships or private foundations looking to sponser students to study abroad.
As others have mentioned you will have to take the SAT Is and possibly the SAT II subject tests. I believe when I applied the subject tests were required. Also keep in mind that US universities weight extra curricular activities, volunteerism etc. more heavily than British schools.
I'm not particularly familiar with the high school system you go through in the UK, but I would like to point out that American Universities are very competitive, more so than UK unis. Be prepared for that. You may be familiar with the GPA system which assigns points for grades on a 4.0 scale. Many students applying today are awarded extra points for AP/IB classes and therefore carry a GPA that is off the scale, in addition these students are prepped intensively for the SAT tests and have been padding their resumes with after school activities since elementary school. I'm not trying to discourage you, just suggesting that you think of insurance schools in the U.S. very carefully if you really want to be there.