The Department of Health and Social Care (DHSC) advise that treatment under sedation should be provided as either completely NHS, or completely privately.
Private treatment with NHS sedation
If the patient elects to have an element of the proposed treatment carried out under private contract, the private treatment and the sedation component must both be provided privately.
NHS treatment with private sedation
An NHS Course of Treatment (CoT) under sedation can only be provided where there's a contract for sedation on the NHS as 'additional services'.