Specialist assessment centres for girls /females with autism?

My daughter is aged 9 and for various reasons (and for a long time) I have thought she is on the autism spectrum. School now agree and I have filled in the initial paper work for an NHS assessment. I know usual waiting times are around 18 months, and currently I expect them to be longer due to everything being put on hold. 

A private assessment is a possibility and is obviously favourable as they can be completed in such a short time. I am however wary of getting her tested in a time where the diagnostic criteria is still so skewed towards male representation.

Is there a particular private diagnosis centre that is well known for being up to date with current research and takes all this in to account when diagnosing Females? I am in the south West of England but could travel if needed.

Thank you in advance for any suggestions