There are a couple of misconceptions on this thread.
Firstly, whilst it is true that there are a number of mandatory vaccinations and blood tests for NHS clinicians, these were not brought in retrospectively. In the first few years of my career, for example, an HIV test was not required before you could start seeing patients. The NHS did not bring in HIV testing for everyone on day one. Instead, new starters had to get occupational health clearance before they started, and they added an HIV test to the requirements of that. The same thing a few years later with Hep C. Now I suspect pretty much everyone has had those tests.
It's certainly possible that a requirement to have the Covid vaccine will be brought in, but it's highly likely that this will be for new starters only, not current employees.
Secondly, for those who are saying you would decline care from an NHS clinician who has not been vaccinated, then be aware that you are unlikely to know this. The only way you could know this is if that clinician volunteered their vaccination status. You have no right at all to know any details of the medical status of anyone who treats you. The fact that they are in post means that they have appropriate Occupational Health/employer clearance to do so. If you ask for any details at all of an individual clinician then they are entitled to decline to say.
OP: I strongly suggest that your partner takes advice from their union, not here, as some of the information you've been given is incorrect. It is likely that a requirement to vaccinate will be a contractual change, and the union can best advise on whether that is something they can impose or not.