Important tips to follow before buying a used car in UK-
1.As per my opinion, used car always have some problems, so if you buy its original owner than after sale he or she will not be able to help you, but if you buy from a reputed dealer then a dealer will help you after sale, as before buy every dealer will check the car or any other vehicle, so if they find any issues they try to fix it .
2.Check thoroughly the registration document,MOT certificate and most importantly the service history of the car.
3.Drive it for a sufficient time and look after its mileage,engine performance,tyres wear and tear .Took the car to your trusted mechanic.
Hope it helps you.