To keep repeating the 7% figure is to be deliberately naïve.
26-30% would be more accurate.
I think your analysis is simplistically binary.
For example Benenden Healthcare is the UK's largest mutual organisation with 950k people covered for a wide range of conditions. I don't think this is covered in your data.
nhs consultant working in the private center is removed from the nhs
All nhs consultants can work in the nhs and privately this was set up by Bevan in 1948. So if an nhs Consultant ops to work in the private sector (thus increasing his salary) the nhs has lost a consulant.