Looking into getting an assessment . Please help

Hi All, I’m 26. I was diagnosed with mild dyspraxia as a kid. My parents,myself and therapist think I’m autistic. I’ve booked a GP appointment to look at getting an assessment. I’m told it’s a very long waiting time. I’m happy to go private but I’m aware that there diagnosis don’t always get accepted. Is there a way to get an assessment private but recognised by the NHS. Thank you in advance