Core crew would be civilian contractors, which as part of their employment contracts would be obligates to crew the ship during a military deployment. The standing medical staff would again civilian, though ideally medical reservists and it would be additional reservist medical personnel who would bring the numbers up to full capacity when needed.
The ship should have one or two embarked helicopters, though these should be leased and manned by civilian crew. Their role would be casualty evacuation to and from the ship as well as carrying out supply missions.
We are not talking about a military vessels here but a floating hospital able to deploy around the world, but which h would have a wartime role, so in response to the question in the title, No, but the UK should have one.