From my experience, NHS areas don't necessarily correspond to the areas schools are in. My DD is now mid-twenties.
From very young, I'd been asking GP for help as DD was "different" to her peers, missed milestones etc. but because there was no support from school I was fobbed off for years until I made a huge fuss and was referred to a NHS paediatric sensory OT. Nowadays, there aren't many of those around.
DD's state primary were useless, "saw nothing" and were oppositional to OT's involvement and did the bare minimum to help dd despite the OT visiting school and telling them what interventions they should put into place to help her. she was also badly bullied there which they did nothing about.
DD's 'Crested' prep was brilliant at accepting what DD's OT said and acting on it even though they were out of county, OT could not visit the school and saw DD in the holidays at home but it worked well. Most of the teachers there were very experienced in teaching kids with a lot of differences, the place was a revelation.
DD's private secondary were much more 'by the book' and asked for a complete private assessment from the local University who had a team to assess for a plethora of learning difficulties, disabilities etc. She was seen there for a full day and as parent I had to complete loads of questionnaires but the end result of that was a comprehensive report which listed all the tests used and her scores. It highlighted all of DD's strengths and weaknesses and gave lots of recommendations for school to follow to support her needs. Their reports and one from a private SLT secured her more time in exams.
In your shoes, I'd read up loads on Dyslexia, Dyspraxia, ADD, ADHD, ASD/ASC PDA and their presentation in girls and women, simply because all of those conditions share a lot of traits. At this stage I'd not worry about the name of the condition she may have, I'd be more concerned in finding someone to test her capabilities in many areas so that her strengths and weaknesses in a lot of areas, e.g.social, sensory, physical as well as academic can be assessed and a report showing those and suggesting interventions can be submitted to school and home.
Where to find a team that can do such an assessment?
Some accept private referrals directly, some only accept a GP's referral even if you are having a private assessment.
As a first point of call, you can ask her school's SENCO if they recommend a particular team to do such an assessment.
My experience was school said she was putting in 100% effort but not getting the results she should be so they suggested a comprehensive assessment carried out at the nearby Uni, but that was because the Uni had a specialised centre for assessments of that type for all age groups, most don't.
For info, this is a how-to for autism assessments including private. www.autism.org.uk/about/diagnosis/children.aspx
www.autism.org.uk/services/diagnosis/diagnostic.aspx
Diagnostic Services www.autism.org.uk/directory/browse/cid=6~aid=1~s=1/search-results/pg=1~sid=2399797.aspx
When you have sorted an assessment for her, before it happens, spend a little time putting together a history of her differences if you can, when you noticed what can be helpful for the professionals. Some of the questions they ask parents go back to early development and nursery/starting school ages, so if you have a think about those beforehand, you may be able to give better answers than I did as it came out of the blue!
In short, ask school what centres they use for assessments, find out if you need a GP referral or if you can just self-refer.
Have a look at other referral centres if you'd prefer to. If you have private health insurance, check your policy, they may fund any assessments.
Do NOT just go for any sort of screening tests because they are considerably cheaper, they are often administered by non-professionals, i.e. they cannot give a diagnosis and can only say there is a likelihood of the child having x condition, whereas a full assessment will be more expensive, very comprehensive and will give a firm diagnosis if warranted, otherwise will identify traits.
I know it's a complicated and frustrating process, but you'll soon pick it up. shout if anything's not clear.