Homework or research time?
Check out the California Department of Motor Vehicles (DMV) web page..
You might all search a bit on the internet -- I noted several California universities had web pages which gave tips to international students on buying or selling a car.
It's not uncommon for cars to be sold in the San Diego area to non-US nationals, so I suspect a dealer won't have any problems with this. A major reputable dealer will probably have all this information at their fingertips as well, but private parties may not. Do your homework just to be sure.
A couple of things to keep in mind..
To register the car and drive in California you need to have a level of liability insurance. If you're buying the car, you'll probably want to bring a copy of your insurance policy as proof of insurance from the UK. You might want to give them a call and find out how extensive their coverage is in the US and make sure it's still good here. (Just to make sure). Having a letter from them as "Proof of Insurance" (most firms have this as a standard form) is pretty much the gold standard for this.
To drive the car in California it has to pass a smog test. California has the most stringent anti-pollution statutes in the US (and in the world, I believe) and almost all cars have to pass a state test of their emissions level every 2 years. If you're buying a car, make sure this test is up to date. If you're buying the car from a reputable dealer they'll handle this if its needed -- if you're buying from a private party, I'm not sure what is needed. But you'll need to show evidence of an appropriate test when you register the car through the DMV. If the car doesn't pass the test then you get a "fix-it ticket" which means you have to go get the car put back in compliance before it can be registered -- go to a mechanics, do some work on the car, replace whatever needs to be fixed. Hence you want this to be resolved before you finish buying a car.
Lastly, are you a member of the UK Auto Club? (There are several branches I recall). If you are, you might give them a call and see if they have a standard packet on this -- and for their driving in the US information packet. There are reciprocal agreements between the US Automobile Association and the UK Auto Club. This may allow you to get maps, roadside assistance, assistance in registering a car, low cost insurance if needed, etc in the US -- including if anything comes up along the way (towing, recommended mechanics, tour books, etc.)