[Make, model, registration number of car]
On [date] I bought the above vehicle from you. On [date] it developed serious defects [describe].
The warranty has expired but I believe I am still entitled to a free repair because the existence of such a serious defect in a car which has only done [number] kilometres indicates it was not of acceptable quality when I bought it. This opinion has been confirmed by [independent expert such as Automobile Association or reputable motor mechanic].
Ordinary wear and tear could not account for the problem so soon in the life of the vehicle. I am a careful and conscientious owner, as the general condition of the car shows. I have not done anything to the car to cause this defect.
Please let me know as quickly as possible what arrangements you propose for rectifying the problem.
Point of Law
Guarantees given by the Consumer Guarantees Act are in addition to any manufacturer's warranty. If a major fault develops - such as a gearbox requiring repairs when a car is relatively new - then you can claim under the Act. Of course, the older the car and the greater the distance it has travelled, the less likely you are to make a successful claim. You must be reasonable in your expectations.