One of the characters is a bus driver, and three buses supplied by MediaBus of Romford appear throughout the episodes in different versions of London Transport red (thanks Ewan Gray).
His main bus is DT1 (G501VYE) a 1990 Dennis Dart with distinctive Duple Dartline bodywork, new to London Buses, but later with London United. I'm not sure it ever went anywhere near Oxford Circus! It's actually driven by Kevin Stuart (thanks Kevin!)
Also seen is RM545 (WLT545), a 1960 AEC Routemaster/Park Royal which began with London Transport but went to London Coaches under privatisation:
The third is a MCW Metrobus in Metroline colours, which may be M443, a 1980 MCW Metrobus/MCW new to London Buses with downstairs luggage racks for Airbus services, but later reseated to standard layout and privatised to Metroline. Confirmation (or not) of this latter would be welcomed, but it's not clearly seen, except in the company of the other two: