Within the NHS specifically, there was the recent case of Alfie Evans[0], where the medical practitioners said there was no hope for him and the family wanted to take him abroad for care. The NHS and the UK legal system decided that his best interests were to die in the UK. His family was not allowed to take him for additional care.
That isn't really an issue with the NHS. If it's an issue it's with the UK's family law which recognises that the parents of a child doesn't always act in the child's best interest and allows the state to intervene.
0. https://en.wikipedia.org/wiki/Alfie_Evans_case