Children under 18 in full time education never pay for dental treatment. I've never known parents having to pay for their kids having braces. Adults yes, but kids no
"The NHS contract for orthodontics funds all braces, adjustments and repairs required during the entire treatment. The only exception is the charge for replacement of removable braces lost or damaged beyond repair. It is not permitted to charge patients under the age of 18 for a brace or any part of the treatment, nor to insist that part of the treatment is undertaken privately before acceptance as an NHS patient. Any such practice is a serious breach of NHS rules which renders the orthodontist/dentist liable to disciplinary action if reported to the local PCT/Health Board or the General Dental Council" - taken from the British Orthodontic society website