I assume you are at the point of choosing whether to apply? If so I think you should go ahead, the interview process and actually meeting the people who'll be working with will tell you a lot more and you can then make a final informed decision as and when you are actually offered the role. If the role is all you say it is then it sounds a great opportunity - clinical NHS people often feel a real reluctance about 'leaving' for the private sector but personally as a long-time NHSer I think there's a place in the system for private healthcare staffed by good skilled people as a support/adjunct to 'main' NHS services (controversial I know!), and also it is good for the NHS for people to be able to take some time out the in the private sector, gain skills and new experience etc. and potentially come back in at a later date. So the below is more questions you should think through out of an abundance of caution and things you might want to ask about at interview, more than reasons to not take it, if you see what I mean?
-When you say the role is more about volume than complexity of cases, is there a risk of becoming deskilled or you losing your confidence with the more complex cases? This could end up being limiting to your career in the longer term if so. If the role is clinical what are the arrangements for clinical supervision and for professional development, will you be able to have/ask for stretching and challenging work as well as churning through lots of day to day stuff or is the company really more looking for a really safe pair of hands they aren't interested in developing further?
-How easy would it be to come back into the NHS after a few years in private, should you want to? Obviously it would be treated as a break in service whatever, so I'm more thinking about how common jobs are in your service area, are there loads of Band 6/7 jobs in your local area or are they few and far between meaning you might have to wait or commute further should you want to come back?
-Do ask about the full 'package' in the private sector jobs, like you say usually the headline salary figure is higher in private, but sometimes things like unsocial hours enhancements, pension, sick and maternity pay are much worse. Also you'll likely lose annual leave, very few private sector companies offer the 33 days plus BHs that NHS 10 year + people get. So do make sure you compare like with like, if the entire salary increase will be swallowed by extra childcare costs because they don't offer flexible working and you'll need childcare for more of school holidays because of reduced leave, it becomes less attractive (although unlike in NHS pay in private sector is usually more negotiable so you could always lay this point out to them and you may find they make an increased offer)...
-This is a worst case scenario, but do be aware by leaving NHS for a new employer you lose most of your employment rights, so in theory if the company felt like it, they could let you go anytime within the first 2 years for pretty much any reason with no compensation due (except notice pay which may well be just 2 weeks or similar). This is true of changing trusts within the NHS as well incidentally, but whereas in the NHS it would be highly unusual for someone to fail their probation (except in clear incompetence cases) or for clinical people to be made redundant, I suspect in the private sector things can be more ruthless and if for instance you were to fall seriously ill and be unable to work, or the company loses business/key contracts they'd be looking at simply dismissing you rather than having the ability to support you long-term or redeploy you elsewhere as the NHS would at least try to do. That isn't a reason to not take the job (otherwise no-one would ever change jobs within the private sector!) but I'd be ensuring you have good critical illness cover for instance, esp if jobs in your specialism are scarce …