I think that we might need a more detailed question to provide a specific answer here. The term 'parental control' is largely absent from English statute law (except, for in example, where it occurs in respect of a child being beyond parental control - in relation to the imposition of care orders - in the Children Act 1989).
Otherwise 'parental control' is simply
one of the individual responsibilities of a person having 'parental responsibility' (or, indeed, of a person acting 'in loco parentis'):
https://www.gov.uk/parental-rights-responsibilities/what-is-parental-responsibility