Look up the Sale of Goods Act 1979 (as amended) and see what that says about what people can and can't do after purchase of a car.
Going through that now after my wife's new car went wrong.
Basically, I think that he can claim a replacement, a repair or a refund.
I'm not so sure about that, I think there are different rules for a private seller.
Edit: http://www.adviceguide.org.uk/index/c_secondhand_cars.pdf
Secondhand cars
When you buy a secondhand car, your rights will depend on whether you bought
the car from a dealer, from a private seller, at an auction or over the internet.
Buying a car from a private seller – what the law says
If you buy a car from a private seller, you won't have the same rights as
when you buy from a dealer. You will only be able to take action against the
seller if:
* the vehicle doesn't match the description they gave you, for example, they told you it had only one owner when it has had several. The seller will be responsible for giving you a false description, even if they believed it to be true
* the seller broke a specific contract term, for example, by saying that the car would have an MOT and it did not
* the car is unroadworthy. It is a criminal offence to sell an unroadworthy car. A car is unroadworthy if its brakes, tyres, steering, or construction make it unfit for the road. An MOT certificate does not
mean that the car is roadworthy
* the seller was not the legal owner of the car and did not have a right to sell it.