I am trying to get Braces at 19?

So yeah I decided the need for braces now and I am aged 19. I went to the dentist last week for a check up and ask about it and he said he would refer me to an orthodontist who would be in contact with me.

Anyway, being 19 I know I have to pay so would I be right in saying any NHS waiting list would not apply to me? Also does anyone have any idea of when I would be likely to hear from the orthodontist? My dentist isn't exactly that local so if I am paying I was wondering if it would be worth finding somewhere just around the corner?

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Edit:

I just read the NHS system on different "bands". I see braces are in "Band 3" which is suppose to cost £204. I go to an NHS dentist so I was wondering if this any relevance to me at all? Or is it covered for those who have a medical need for them?

Thanks