I don't know.So do all doctors agree to be “in network?” Do they all get paid the same amount?
I work in the financial services industry.
We also have a private medical sector, with a major provider being BUPA. That's where you can pay extra or it's a perk with some jobs, to go private and cut waiting lists for certain treatments. Feel free to have a search, I don't have specific examples at hand.
It can also be the case that certain operations and procedures are outsourced by the NHS to the private sector when they are particularly busy or don't have the skills.