Private Diagnosis or wait for CAMHS

Hi, I'm new on here and looking for some advise.....where to start?......my son who turns 5 in Feb has always gone to a private day nursery since he was 7mths old and during his time there they picked up on a few things like he wouldn't play with other kids share limited talking etc. Early years became involved and he then had a little extra 1 on 1 help & we started to see a SLT. He was then seen by an educational Phycologist and was then recommended to start main stream local school with an EHCP, he started on 5th Sept and lasted 4 weeks there, without going into detail they were useless and had no want or desire to work with him so after popping in and seeing how he was being treated I decided to pull him out which I'm sure they were relieved by!  The school referred him to camhs and I have had the app for Jan but am being told by CAMHS that although he will be seen the. It could be months before they Diagnosis. I have searched the net and found someone willing to see us with a view of private Diagnosis on 8th Nov for £1000 has anyone had a private Diagnosis and would recommend that route? Many thanks