At 16 you sign your own NHS form for dentist or opticians, a young child is unlikely to be seen without parent on premises but though now an early retired dentist I would often see children 6-7 in surgery while parent in waiting room either with other siblings or because sometimes child deals with treatment better without parent especially the parents who do unhelpful and inaccurate running commentaries, often high school kids would come for check ups alone after school, if they needed treatment they would come back with parent or I would ring parent or if 14-16 and I judged them competent to consent fully I would treat with out parents, some kids would have been in pain for weeks if I said I wouldn't treat without parents being there. Most children over 13 are perfectly capable of giving informed consent to a dental check up or eye test, however they may not be able to completely judge something that maybe painful now but will have benefits in 10-15 years time