I've worked for the NHS for a couple of years and I start a new job with them in August. You have to remember that it's still pretty hard to get a decent job as a young person in many parts of the country.
When I was first applying for NHS roles back in 2012/2013 I must have applied for nearly 100 jobs (of a wide variety) and got three interviews, the last in which I was successful.
When I started applying again a couple of months ago, I had two interviews from two applications. The difference this time was that I had two years experience in the role I was applying for. I am convinced that without my experience I would not have had interviews. My friend who has the same degree as me from the same institution has applied for similar roles to mine but has had no luck. And that is with three years of management experience in retail.
At one of the interviews I finished fifth and the woman who rang to tell me I had been unsuccessful explained that they had never seen such highly qualified candidates (most with degrees and solid experience) applying for such a basic and unqualified role.
Therein lies the difficulty in applying for jobs with the NHS. As they are such a popular employer you will most likely face very strong competition (as in most jobs in the country) for every role that you apply for. Your chances are maximised in roles that you are slightly overqualified for, are relevant to your degree and are relevant to any experience you have, within the NHS or not.