How to get a diagnosis

My husband and I are trying to get an autism diagnosis for our 9 year old daughter. I went to the GP who said they no longer do referrals and this must be done via the school. We’ve had a meeting with the school where we highlighted a list of symptoms and her class teacher is doing the same. We’re meeting next week to discuss what plan can be put in place at school. However she doesn’t have any issues at school, her symptoms are more general anxiety and in social settings. What I really want is a referral to a specialist but that doesn’t seem to be being offered.

Does anyone else have any experience like this?