Denied NHS Diagnosis - support for second opinion?

I posted recently about my first assessment experience. Today they confirmed that in their team's opinion, I only meet 2 of the 3 DSM criteria and therefore do not merit a diagnosis.

Their reasoning boiled down to the fact that I've learned to consciously think about and understand social interaction, and because they only had time to ask about a handful of my relationship experiences (across almost 30 years) they've decided that, because I can understand my parents fairly well after living with them for years, I display no issues with understanding communication.

One of the team did say to me, and I quote, that 'it is just not possible for a person with autism to learn to communicate very well or think about other's feelings'. In the activity where you watch videos of two actors and are asked why the people are saying/doing what they are, I prefaced each answer with 'I don't know because I'm not them', before suggesting several possibilities which I had to think about first.These answers were based on logic and my own past experiences, not intuitive. They said because I could think about why people might say certain things and guess the correct answer (amid a handful of other answers) I don't display issues with understanding communication.

I asked if they had considered any of the other relationships or experiences which they hadn't asked me about, they said they had all the information they needed (based on one appointment, a telephone interview with my mother and a few letters from me about some of my history but not all). They seemed overall very annoyed that I had given them so much extra written information (which was cut down when I sent it, because I assumed as specialists they would't need too much extra info). They suggested I go back to my GP and try more counselling and CBT, of which I've had courses of over six times since adulthood.

They said my Sensory Processing Disorder (diagnosed in childhood) was an entirely seperate condition and not related to autism. They said my need for routines and my highly focused interests were essentially personality traits, and not necessarily related to autism.

One of the team said, and I quote, 'there is no workplace/jobfinding support for anyone with autism just because they have a diagnosis'. She also said this was the case for therapy and other services. I asked if she meant locally, and if she was considering whether individual charities/employers would provide help (which I have seen evidence they do), but she just repeated her statement. They did not discuss the fact that I've been unable to work for almost 5 years because of increasingly debilitating social anxiety, or the constant issues I experienced with communication/bullying when I was in work.

My mother and my advocate were both present for this appointment and they said afterwards they got the impression that this team did not know anything about autism at all, or at least had only experience of very low-functioning individuals (the team said I was of almost genius-level intelligence, so I don't know if they can even understand a lot of what I'd written). My mother and I verbally confirmed we would be seeking a second opinion, and they said I would have to get it from my GP as they do not seek opinions from other teams (though NICE guidelines recommend they do so). My mother was crying during this time because she felt what they were saying was so incorrect.

Overall, I want to know if this experience seems as unprofessional as I feel it was? Does this sound like a proper assessment process?

I will be waiting for the report, and then going to my GP and possibly contacting NAS for assistance. But I feel even with a different team of 'specialists', they may be just as unequipped to diagnose properly as this one was, especially on the overstretched NHS.

Any advice appreciated.