Hi Andy
Sorry to hear about your predicatment.
Although I'm not an expert on the type of injury you have, I do not think that it is fair to offer you no real resolution to your injury.
Many consultant surgeon will leave a problem alone if it is not causing the patient too much trouble, but when it starts causing the patient to have problems with your daily living activities, the situation really should be taken more seriously.
I certain would hold fire going private at the moment, at least until you find out WHY an ACL reconstruction cannot be done, there may be a reason and by going privately you may be wasting your money or at best, being in a worse position than when you first went to the GP.
Best of luck & lets us know how you get on.
Iona x