I had the same thing when I bought my car, it isnt a problem, what you need to do is pay the money you have agreed to pay for the car directly to the finance company. If this is less than the total amount then you should make sure that the person who is selling it pays the amount left over before you part with your money. It will take a few days for the finance to clear. The seller should give you his account number and all required details so you can contact the finance company directly. Once funds have cleared the finance company should be able to fax/send you a letter confirming the account being clear, you should keep a copy of this and give a copy to the seller at which point the car should be handed over to you.
Make sure you pay a deposit to the seller and get a receipt of this and write down how you will pay the rest of the money and once cleared you will own the car and then sign this and get the other guy to too, this should cover you enough in case anything goes wrong. If you have a signed 'contract' and receipt for deposit and you have been to the sellers house to see the car, you should therefore have his name and address. If he doesnt follow through you'd have enough to go to the police with. But in my experience everything rang smoothly, I had regular contact with the seller and we told each other what was happening.
Really isnt anything to worry about, it's quite normal when buying a car from someone who bought it new and have finance through a finance company.
Hope this helps