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
'Around 36 million Europeans [or 1 in 30] may have experienced #LongCOVID in the first 3 years of the pandemic, announced @hans_kluge @WHO_Europe, latest @IHME_UW 'A glaring blind spot in our knowledge that urgently needs to be filled'. #LongCOVIDcontinues
https://www.healthdata.org/news-events/insights-blog/acting-data/long-covid-serious-health-concern-europe
Long COVID is a serious health concern in Europe | The Institute for Health Metrics and Evaluation

Nearly 36 million Europeans – or 1 in 30 – may have experienced long COVID in the first three years of the COVID-19 pandemic, announced the World Health Organization (WHO) European regional director Dr. Hans Kluge, who cited the latest estimates by the Institute for Health Metrics and Evaluation (IHME).   

The Institute for Health Metrics and Evaluation