I would say apply. It probably depends on your location nationwide, but in London/South East I found the recruitment market very open when recruiting at lower bandings.
The calibre of applicants had started to get better in the past year or two, but nothing too prohibitive.
In terms of having recruited corporate people into the NHS, I would suggest emphasising your transferable technical skills and also any experience of working collaboratively and managing teams to deadlines.
Also it isn't difficult to do a bit of research into the main datasets that the NHS manages. Its fairly jargon-y, but most people learn on the job.
I would give it a go - the worst that can happen is they say no, and you're no worse off than now.
Also, don't give up after one application. Sometimes I would get too many applications - over 50. Then a similar job a month later - one or two serious applicants. Different organisations also experience very different response rates, depending on factors like location, convenience, how high profile they are. So all of that comes into play in how likely you are to be successful.
Good luck if you decide to do it.