When you buy a car privately, you have fewer rights and parts of the Consumer Rights Acts don't apply. For example, there is no legal requirement for a car to be of satisfactory quality or fit for purpose. But contractual rules about misrepresentation do apply, so the seller must accurately describe the car and not misrepresent it (i.e. he must not lie to you about its history and its reliability etc). The onus is on you as a buyer to ask the questions and inspect the car before the purchase. The seller doesn't have to volunteer additional info so if you don't ask lots of questions you may not get the full story. Whether or not you stand a good chance at small claims depends on whether or not you can prove the was misrepresented and/or the seller lied to you when answering your questions.