Sorry you have this the wrong way round. A fifteen year old can consent to treatment, they cannot refuse treatment, in that case the parent's consent would override the child's refusal. There have been cases where the child has gone to court, been made a ward of court which overrides the parental rights and the court has agreed with the child's desire not to be treated, but that is the court not the child refusing consent.
The cases around a child's consent to treatment arose from teenagers seeking contraception, they could consent if competent (Gillick competence) and parental consent was not required.
https://www.medicalprotection.org/uk/articles/eng-consent-children-and-young-people
* Of course the UK does not have a unitary legal system I refer to the law in England and Wales, which is what I assume you meant. The law in Scotland is less clear but probably a Gillick competent child can refuse consent, but this would likely be tested in court.