Hey there,
You've had some good advice here so I'll just add a few more things. I'm from LA, so I'm qualified.
www.westsiderentals.com - it will cost you 25 pounds to join and it's good for three months. It's like findaproperty.com but nearly every rental is listed on it and there are no further fees - no estate agents for rentals in Los Angeles. craigslist is also good but pretty much anyone serious about finding an apartment will join westside rentals. Also, very few flats come furnished. you will pay a premium for that. You can rent furniture, however. There are a number of companies, try a google search.
Ditto other comments on the car thing. Traffic SUCKS all thru LA, but it's no worse than London. Thing is, public transport is for scary people (except in Santa Monica right around the water.) You want your own car, cheap is fine. Hell, you can get (and not pay) all the parking tickets you want if you're just there for three months... Your car won't get towed that quickly!
Most important thing is to live very very close to UCLA. This is a quality of life issue. Otherwise you have to add an hour commute each way, no matter where else you live. I lived two miles from work and it often took me 45 minutes to get home. Did I mention traffic SUCKS in LA?
Re cycling - there's awesome cycling near the beaches but no easy way to get to UCLA unless you're used to cycling in London, in which case it will be a piece of cake. uhhhh, after you master riding on the right side of the road!
Hope this helps a little. Oh, and don't forget to learn to surf while you're there. Venice Beach, baby!