Many people have the relevant health checks carried out on their pets even if they do not want to breed.
As it is expensive though many people understandably do not as it is not a requirement.
Breed clubs will have a list of the health problems that pop up regularly in their breed, hip dysplasia, elbow dysplasia, VwD (blood), DCM (heart), Dermoid Sinus (skin) as well as all the different eye problems that can occur.
There are approved eye testing panellists listed around the UK but it is cheaper if you can go to a day organised by a breed club, but there is usually an eye tester fairly near you.
Anyone can x-ray hips/elbows but many of us prefer to go to those that specialise in this area.
It is not necessary for the dog to be a pedigree or even licensed with the KC.
More info about these here: