The NHS effectively subsidises private health care by picking up the pieces when patients become too ill for the private clinics/hospitals to deal with.
The Centre for Health & the Public Interest finds up to 6,000 patients a year are transferred from private to NHS facilities due to complications (& these are only the direct transfers, not those after treatment) costing the NHS at least £250m a year.
The NHS should be (at the very least) paid for these 'rescues'!