Referred for private assessment

My background: the first time I became aware that I might have ASD is when I was sent for an assessment aged 13 but my mum lied a lot to the psychiatrist. Now I'm 20 and I have a white collar job.

A while ago I was being seen my a CMHT because of depression and anxiety. They suggested that I might have ASD but there is no funding for adult autism diagnosis in my borough. 

I have been experiencing difficulties at work relating to change, communication and sensory issues (noises and smells),  but my manager and HR department are relcutant to do anything about it because I have no diagnosis (of anything at all).

My Occupational Health department have referred to a private psychaitrist for an assessment. Does anyone know what this will involve, and where I will go from there?