Classic car purchases from a specialist dealer are covered under the Consumer Rights Act - which means the car must be of satisfactory quality (often in accordance with the price paid, mileage etc), fit for purpose (e.g. if it's a historic race car), and as described. It's the latter point where most of the problems arise. If a defect is discovered, you have 30 days to reject the car and get a refund - after that the buyer can request a repair. If you're worried about buying a classic then make sure you do your homework. You can always join the relevant marque club and ask one of the more technically-minded members to help you inspect a car.