Quaint as it may seem compared to the modern system of communication, the world was relatively wired telegraphically by the time World War One broke out. Britain could send a message to Australia, for instance, via the USA, across the Pacific, where cables had been laid. Or across the Atlantic to Brazil, then over again to Africa, then across the Indian Ocean to India or Australia (for instance). All but the most far-flung parts of the empire were connected this way by 1914. In fact, most places had been connected to the home island by the late 1880's. See more here (http://www.porthcurno.org.uk/nerve-centre/empire)

Immediately after WW1 the Imperial Wireless Chain was put into place, a system of wireless telegraphy connecting the Empire.