Medical treatment without consent is assault and can only be considered if a court order is in place.
That is true of someone with capacity. It is an offence under both common law and the HSCA 2008 to treat a patient who has capacity without their consent, other than when they are unable to express it (e.g. a coma) or detained under the MHA etc.
The position WRT non-capacitous children is less clear. AFAIK, there has never been a criminal prosecution of an HCP for treating a child without parental consent. Professionals - not just HCPs, but teachers, childcare workers etc - do things to children all the time without consent from either the child (too young) or parent, which would be assault if you did them to an adult - from helping a Reception-aged child who has wet herself, to helping a child tuck its shirt into its trousers, to putting a dressing on a cut knee. You cannot extrapolate what is allowable for an adult and apply it to a child.
Court orders are typically sought when a parent opposes a medical intervention, or when parents disagree (strictly speaking, only one parent's consent is required but HCPs are unlikely to proceed with major procedures if the parents disagree).
A parent actively opposing a treatment is a very different situation from simply not having obtained parent consent. Otherwise paediatric wards would be unable to function. HCPs don't seek the parents' consent every time they take a blood test from a neonate on NICU, or give pain relief to a child, or 100s of other common interventions. Typically, active parental consent is sought for surgery, vaccinations, and major interventions, but not for minor, commonplace ones.
If it were assault to perform medical interventions on a child without securing the parent's consent, every paediatric HCP in the country would be in jail.