The story is based on a late 19th Century legend known as the Vanishing Hotel Room. It previously served as the basis for one of the segments of Eerie Tales (1919) and So Long at the Fair (1950).
Alfred Hitchcock did not begin his introduction to this episode with the usual "Good evening..." However, as this was only the fifth episode of the series, it's possible that the "usual" introduction had not yet been established.
This takes place in August 1889.
In his introduction Alfred Hitchcock states explicitly that the same story forms the basis for The Lady Vanishes (1938), which was directed "by no less a personage than, er, Alfred Hitchcock!"