Thanks to all that have commented, I really appreciate it 
I was shocked at how short their list of requirements for the role were. Something like 'ability to manage time well' and 'good on computers' were literally along the lines of what they were asking, and worded just as simply.
I have been selected to take their competency test. I completed it this evening. Fingers crossed!
I'd go for higher band jobs expressing how you've worked for difficult consultants and are used to the high pressure, fast pace, constantly changing deadlines.
It's a tricky one. Most seem to specifically ask for working for experience working for directors, CEO, etc. So before I can even explain that, it seems I'm out.
I've applied to a lot of them anyway since you don't really get PA roles like that within an NHS setting, they're extremely rare.