We'd always assumed that this war was known as the Great War until WW2 came along at which point it was renamed as World War One or the First World War. But the term was first used in print in 1920 as the title of a book, 'The First World War' by Charles à Court Repington. He was using it to emphasize the global nature of the war rather than its sequential nature.
Different memorials give different years for the end of WW1. The Armistice came into force at 11am on 11 November 1918 and fighting ceased on the western front but hostilities continued elsewhere and the peace treaty was not agreed and registered until 21 October 1919. Note - it seems to be just a lucky poetic chance that the Armistice coincides with "the eleventh hour of the eleventh day of the eleventh month". Kaiser Wilhelm abdicated on November 9th, presumably not thinking "that allows just the right amount of time for a poetically-timed Armistice".
For some signs of WW1 on buildings in London see Spitalfields Life.
