Assessment Refusal

Hi, first time posting! I’ve been under CAMHS since I was a teen where it was first suggested that I was autistic but I immediately dismissed it as I was a kid and was scared of being labelled as autistic as I didn’t understand what it was. I was therefore treated for depression and anxiety. It was also recently suggested that I was autistic by another psychiatrist where I was receiving help for mental health issues, she suggested I go to my GP for a referral which is what I did. My GP did send the referral but the autism assessment place has refused to even assess me as they say it’s down to social anxiety even though I have numerous autistic traits that are nothing to do with social anxiety. I’ve tried twice now to get an assessment on the NHS and twice they’ve said it’s just social anxiety. I can’t afford to go private but I’m not sure what I can do. Can I ask to be referred to a different service? Looking at the reviews on the place I was referred to im not the only one who they’ve done this to and others have been told similar and have then gone on to get a diagnosis. Any advice would be appreciated