I take note of the expressed opinion that the euphemisms are not well known in Britain and have prior knowledge that the most likely candidate for the origin of both uptown and downtown is the early development and direction of new construction on the island of Manhattan, New York City. As the city developed it could only expand in one direction, which, obviously was "up". That is, towards the higher or northerly end of the island. This became known as the more desirable area in which to build a new business as well as new residences. Those doing so then could only refer to "lower Manhattan" as, you guessed it, "downtown". Other cities latched on to the descriptions but it still, apparently, remains an Americanism... (The first print edition of the terms was ca 1825-1830). Other descriptions are now almost as ubiquitous, i.e., "Upper East Side" and "Midtown Manhattan"...