Need a private assessment in North West, any advice ?

We think our 17 year old son has Asburgers and have done so for or a long while but having being messed about by Camhs for so long they have now told us he is to old to assess/treat and we have to go it alone.  He now has a 6 month old baby son and the mothers family are stopping our son from seeing him due to his mental issues, anger etc, we are hoping a diagnosis will help everyone understand his issues and he can start seeing his son again, he has not been allowed to see him for 5 months and it is killing him, only problem is waiting lists are so long, his son will be one by the time he gets assessed so we have no option but to go private but have no idea where to look or how much it may cost.  We live in the Warrington area