When you buy a used car from a private seller as opposed to a registered dealer, key parts of the Consumer Rights Act do not apply. For example, there is no legal requirement that a car be of satisfactory quality or fit for purpose. The seller must accurately describe the car in any advertisements and not tell you something about the car which isn’t true. The car must also be roadworthy and the seller must have the legal right to sell it to you.
In other words, the car must work, meet the legal requirements for being driven on public roads, and be owned by the seller.
However, when you’re buying from a private seller, the onus and burden is on you as the buyer to ask all the right questions before making the purchase. The seller doesn't have to volunteer extra information so, if you don't ask questions, you may not have the full picture of the goods' history or be aware of any potential faults.
Therefore, when purchasing a car from a private seller, you should make sure that you ask questions and request information on the car before purchasing it. Failing to do this may result in you not being able to return the car and get a refund.
If you’d like further information about the sale of goods, you can always Ask a lawyer.