Try for a personal loan at the bank first, if you've got cash then you can buy from anyone....including privately.
More choice of cars, also she wont be subjected to Payment Protection, Gap Insurance, Extended warranties, and a whole host of other associated stuff she may not want or need.
Most car salesman will try and sell you finance at a higher percentage rate, this is usually negotiable, dont answer the question how much can you afford each month? They could offer an affordable deal but with a subprime company who will be lending at a higher interest rate.
If she has failed clearance with a reputable lender it may be worthwhile getting her Credit History
checked, just in case there is a mistake or something at the property she is registered at that may have been overlooked or is out of date and needs removing.
Money SuperMarket is pretty good at finding finance options.