Total number likely to rise before it starts to come down, so why not increase resources within the NHS?
After all, the private sector wouldn't exist without its NHS consultants, NHS referrals, and its ability to send recovering patients back to the NHS? https://www.bbc.co.uk/news/health-66319064
NHS to expand use of private sector to tackle waits

Ministers in England want to unlock spare capacity, but Labour accuse them of dither and delay.

BBC News
@JoePajak Absolutely right. The private sector infrequently has the resources to deal with serious acute events.