Hello. Yes, it is possible to transition from being a medical person to someone who supports other functions in a NHS organisation through delivering a H&S role and many have done so. In many instances, persons with on the ground experience can offer a lot of value in a H&S role. However, ideally they are best advised to top up qualifications with those that have a H&S focus.
A good place to start would be:
NEBOSH General Certificate
This could open the door to a very entry level role.
Longer term though, it would be preferable to complete a degree or diploma that would help achieve Grad IOSH and put the holder on the path to Chartered Membership.
For example this could be:
BSc in H&S from a recognised Univesity (2 to 4 years to complete)
NCRQ diploma (6 to 18 months to complete)
British Safety Council level 6 diploma (1 to 2 years to complete)
NEBOSH Diploma (1 to 2 years to complete)
Post Grad Diploma/Masters Degree (MSc, MRes, MA) from a recognised University (Usually 2 to 3 years to complete)
There are no short cuts unfortunately, although sometimes there is a bit of luck involved with being in the right place at the right time and being able to develop some experience in a role, before undertaking any substational further study.
Most NHS trusts have large estates/facilities teams where H&S is a fundamental consideration. There are many H&S Advisors/Officers/Managers to be found supporting these elements of NHS organisations.
From an operational point of view there is usually an Occupational Health department - but that is generally a different career path.
Also, there is patient safety and medical practitioner safety, which I suppose is another topic altogether, and H&S is built into the various protocols etc. There is sometimes room for H&S professionals to get involved with this - although strictly speaking, persons with a medical background are better suited for this.