It’s already happened
James Meek: The NHS Goes Private, 22 September 2011
“... one of America’s largest private health companies. Mark Britnell, a career NHS manager who rose to become one of the most powerful civil servants in the department, upped sticks in 2009 to become global head of health for the consultants KPMG. This last move did have the advantage of giving an insight into what had actually been going on in Whitehall ... ”