I've just paid (quite a lot) to have a new knee.. In the next room was a chap who'd jumped through all the hoops and got onto the 18 week wait list but as the 18 week deadline was nigh the NHS paid for his op in Spire.
It was a bit galling for me having paid, but I got it done a good year before I would have as mine wasn't standard arthritic collapse, I only waited 3 weeks (4 from seeing my doctor)! There was practically no chance of last minute changes or cancellations. Etc,etc.
It seems to depend on your health authority how hard you have to push to get NHS funding for private care, but its certainly available. It may be worth ringing round your local private providers' and asking the receptionist. These lovely people are pre-programmed in niceness and honesty in my experience. Ask nicely and you may find out if there's a chance for your son through the NHS or should you try to raise the money and how much would it cost. Don't give the impression you're loaded and willing to pay regardless and they may well tell you what you need to know.