My daughter was diagnosed by this lady, Dr Maite Ferrin. She specialises in ADHD in girls - as with autism, they can present very differently to boys.
It was £850 for the full appointment (2.5 hours, plus the Connors psychometric tests for school and parents prior), following a QB Check which was, I think, £195, showing strongly that she needed that assessment.
We were lucky in that she is impulsive and hyperactive, not just inattentive. That makes life tricky for school, and so they were fully on board. I'm solely inattentive, and was extremely academic as a child, so I wasn't diagnosed until adulthood. The difference medication can make in life is just extraordinary and I can't strongly enough support proper assessment and, if indicated, medication. Nobody would expect a diabetic to manage without it, and untreated ADHD can be dangerous, given the risks for someone who doesn't notice what goes on around them, or takes risks without being able to weigh them up first. That's without considering the risks that shaming over behaviour the child can't help will lead to real problems with self-esteem, and then to self-medication. I was lucky, and my self-chosen drug was only caffeine. Others aren't.
She may just be absent-minded and flaky, and that's fine. She'll mature as she grows. But if she has ADHD, or indeed ASD, then she needs help. My life would have been so different, had I had it as a child.
I would note that the masking etc may mean she's autistic - again, that presents very differently in girls. You need someone to investigate, as you can't support her without understanding what is going on.
I will also add that, sadly, we also went private because the local NHS failed our autistic son for many years. Underfunding is the root cause, but at present in many areas there essentially is no NHS care for children with these problems. You're lucky if you see anyone, and when and if you do, they are highly unlikely to be specialist, so it's a waste of time. We fund their care on nought per cent credit cards, and quietly thank God for decent salaries.