Because the U.K “isn't” America. We do have buses that convey children to and from their schools, but they're usually standard buses or coaches that are used for service work when not required for that specific job. Local authorities contract them from the companies that run their local networks.

London does not have a fleet of yellow "American-style" school buses primarily because of its exceptionally dense and integrated public transport network. Most secondary school students in London (nearly 50%) use the regular Transport for London (TfL) bus network, where children under 16 can often travel for free or at a significantly reduced rate with a Zip Oyster photocard. This system is far more cost-effective for the city than maintaining a separate, specialized fleet that would only be used for two hours a day. Additionally, London is a highly walkable city with a "catchment area" system that places many primary schools within walking distance for families, with over 60% of primary pupils walking to school. While "dedicated" school bus services (Route 600 series) do exist on specific high-demand routes, they are standard TfL buses that simply change their destination signs during school hours. The urban design of London, with its narrow streets and high density, makes large, dedicated school buses logistically difficult compared to the flexible, existing public transit infrastructure that serves the entire population.