"Monopoly power" is not a monopoly and in the UK, public schools are actually private schools, so maybe we shouldn't compare terminology across countries.
"Courts do not require a literal monopoly before applying rules for single firm conduct; that term is used as shorthand for a firm with significant and durable market power"
That’s because competition/antitrust law, be it UK, EU or US, doesn’t care about whether an entity is a “monopoly” or not. It cares about whether a company is engaging in anticompetitive practices or not. The market share is a red herring.
