Owning a car and motoring in the U.K. is one of those things I really appreciate. It's a breeze compared to other European countries and even compared to California.
First off, you can forget about getting finance. It won't happen. But you're so much better off with a user car anyway.
The U.K. used car market is huge and very competitive. The result is bargains galore. In fact, if you're staying more than a month you can buy a used car cheaper than you can rent one.
When my wife and I used to come here just for the summer we would buy a used car and even if we couldn't sell it at the end we were better off. Summer 2003 we bought a used Honda for 300 pounds from an Australian expat who was returning.
It was a beautiful car (the sunroof leaked but it was summer and 2003 was a dry one). At the end of the summer we drove it to the airport (saved the taxi fare) and gave the keys to a young security guard... it sure was his lucky day!
Another time we drove the car to the airport, put it in long-term parking and hid the key and parking ticket in a magnetic box under the frame. Three days previously I had put the car on eBay. By the time we got home we had a buyer and told him where to collect the car. We actually made a profit on this one!
You don't have to have a banger. If you're not fussy about make and model you can get a 10 year old car with low to medium miles for 300 pounds. I've done it a half dozen times and I always sell it for around the same price. I highly recommend eBay for this purpose.
The other U.K. advantages that make this possible is the ease of car transfer, licensing and insurance. Even the first time I was able to get insurance with a single phone call. You just need a U.K. address. At that time I didn't even have a U.K. bank account. And I only had a California driving license... good for one year in the U.K.
Ownership transfer? Piece of cake! Just send in the form... not even tax to pay! The only time you're taxed is when licensing comes due, not every time you buy or sell a car. In California I had to pay 6% tax (it's probably more now) on any car I bought.
So don't sweat financing... even if you could get it you'd pay more financing charges than the car is worth! If you really want a neat car then budget for a grand. Of course you can get by for a lot less if you need to.
Motoring really shows up one of the mysteries of U.K. life: some things can be so petty and regulated while others are inexplicably laissez-faire.
The property business (real estate) is a similar example. In California it's regulated to within an inch of your life... real estate salesperson's license, broker's license, classes, continuing education, fees, fees, fees...
In the U.K. anybody can be an "estate agent". How refreshing (but, naturally, buyer beware!). Same goes for builders. Anybody can be a builder here but in California you need a "contractor's license".
Oh well, that's enough of my rambling... go and buy yourself a nice banger!