Where the law stops, and what follows
The articles above set out who may prescribe, who may inject, what must be told to a patient and which parts of the regime are in force in which nation. None of them decides who pays when a treatment causes harm. That is a separate question of civil liability, and it turns on employment status, on the prescribing arrangement and on what the records show: it is covered in who is liable when a cosmetic treatment causes harm.
A regulator can restrict a registration and a licensing authority can close premises, but neither can award you compensation, so the body you approach depends on the outcome you need and the nation you are in. The routes are compared in cosmetic treatment complaint routes across the UK nations, and the immediate steps are in what to do when a cosmetic treatment goes wrong.