Is there a British version for the expression "medical exams"?

Depends on what is meant by an exam. If you mean going to the doctor to get checked over, it can be referred to as a 'check up' (which is usually being looked over for general healthiness), 'going for tests' (where something physical happens such as blood tests or biopsies), or 'going for a medical' (which usually suggests that health is being checked over for something specific such as for insurance purposes).