The NHS already contracts a lot of work out to the private sector.
I've had an MRI which was supplied by some South African outfit, my knee was replaced in a private hospital paid for by the NHS, blood tests and bone marrow biopsies sent to external laboratories, offered physiotherapy done by a company paid for by my GP's surgery, and I recently had a call from a company, on behalf of the NHS, asking if they could send me all manner of kit so I can record everything regarding my illnesses and send them the results so they can in turn report them to the doctor. I told them to go swivel on that. I also know my GP's practice outsources all their podiatry work to a company in another town. I've been through A & E a fair few times recently, and a lot of the ambulance crews comng in there were sub-contractors using their own company's ambulances.
If privatisation can improve health care at the same cost to the country, or even cheaper than the NHS's own resources, then why not?