A contract can be verbal - it does not have to be in writing. So in principle you could take the person you got the car for to Court and claim your money back.
However, you would have to prove to the Court - on the balance of probabilities - that this contract was in fact made. If you have nothing in writing at all this will be difficult if he denies it. Are there any witnesses who could support your statements? Was anyone present when you discussed this? Did he pay you (or the finance co.) any traceable money at all (i.e. money which went through a bank account)? Who was the registered keeper? These are just examples - you need to think in detail about all that happened & see what there is that can be used in Court to substantiate your case.
You must also remember that, even if you succeed in Court, you will not necessarily get your money. It depends on the person's financial circumstances - if you know he has little or no income & no assets (such as a house with equity in it) then you will probably be throwing good money after bad in going to Court, because you will have to pay a Court fee to start the case.