Your challenge is, without wanking Britain and with a P.O.D. after October 22nd, 1922, to create a world-wide public broadcasting network. Either dominated by the BBC, or a cooperation of several public broadcasters is up to you, Let me start with it:
The early BBC focuses on serving the whole commonwealth, reaching out to Canada, Australasia and India, becoming more of a commonwealth service. After World War II, the founding states of the EU start to found their own version of the BBC, the European Broadcasting Company (EBC). They cooperate with the BBC however.
In the 1960's, the BBC evolves into the Intercontinental Broadcasting Corporation, with IBC 1 being the main TV-Station in UK, Canada, Australia, India and countless other states (There are regional versions of course). At the end of the decade, the EBC and the IBC merge into the World Broadcasting Company, a name now seen appropriate since the WBC broadcasts on all continents. In the 1970's, PBS from the USA joins the network as well (Although this is rather smart attempt to get quality programs from Europe, to compete with the "big three"), Japanese NHK joins later on. After the fall of the Soviet bloc, the Eastern European broadcasters seeked soon the corporate umbrella of WBC, only Russia is reluctant to join the WBC.