This will depend on what your medical training or qualification has covered. The reason we don't have a blanket exemption for medical, nursing or allied health professionals is because post-graduation the areas of expertise are so broad. For instance, nurses often specialise in a specific area where they will have a great deal of knowledge but they may not have all the other first aid knowledge in the syllabus. Paramedics now work in a much more diverse range of areas and not just in ambulances, some of these are not hands on clinical areas.
This view is in line with some of the large awarding organisations of professional first aid qualifications who ask professionals to provide them with evidence of experience in a field relevant to the first aid qualifications they deliver.
This doesn't mean that every Doctor, Nurse, Paramedic, Physo etc needs to complete a full FR course. The person validating the training just needs to speak to them and identify any learning needs. This could be a full FR course or it could be a discussion with a FR trainer on a specific subject or it could be that no additional learning is required.