At the moment, I would be realistic. Don't expect to go in at the same level as you are on now. You might find that you will have more success applying for roles that are below where you are now. My trust seem to prefer PAs who have already done NHS admin/clerical roles.
I was a PA for a long time in private sector and now work in a clinical role. I wouldn't do an admin job in the NHS. There is a very strange hierarchy where clinical staff trump admin in terms of opportunities, training and pay. Qualified clinicians also seem to assume that admin is a doddle yet I know that many of the admins struggle with huge workloads and outdated systems. Unfortunately, because salaries are quite low they do not always attract the cream of admin staff so expect an inflexible "we've always done it this way" approach. Also be prepared to expect broken office chairs, dusty offices, inadequate stationery, incompetent IT helpdesk, etc.
Despite this, I like the NHS. It's straightforward. It does what it says on the tin. They don't mess you about. They don't advertise jobs that don't exist. They tell you the salary range. They tell you if you are successful at interview generally the same day or the next day. Do I prefer it to private sector? Probably not, it's just different. I don't feel like I am saving the world. I'm just doing a job and getting paid for it in the same way I did when I worked in private sector.
If you apply, you'll need to write a personal statement rather than a covering letter. Best approach is to address all of the items on the person spec with examples. NHS interviewers love a bit of detail! I wouldn't address the values but make sure you align your language to fit.
I wouldn't mention the accessing mental health services unless it's relevant to your application. Even with the NHS, I would be careful about disclosing mental health problems.