The title of the film derives from the Stewardship of the Chiltern Hundreds, which is a position taken by Members of Parliament in the UK in order to resign their seat. The process is an archaic but necessary one given that MPs are not technically legally allowed to resign their seat. Instead this uses the principle that MPs cannot hold a crown office and therefore taking this office removes them from being eligible for the position. A "Hundred" is an ancient administrative area (smaller in area than a shire) and the specific area this role is linked to is located in the Chiltern Hills of southern England.
William Douglas Home's play "The Chiltern Hundreds" had its title (incomprehensible to Americans) changed for the US market. The Broadway stage production, however, had a different title-change to this film version; it was called "Yes, M'Lord" for its brief run.
The events portrayed occur in mid-1945, including the UK General Election, campaigning for which ran from June to July, with results being announced on 26th July. When Lord Pym and Mr Beecham go to submit their nominations for the subsequent bye-election, the newspaper Mr Beecham is reading has the date 1st August 1945. Later on when campaigning is shown part of a newspaper is shown which includes reference to an "atomic bomb" and an attack on Japan (Tamuziru) indicating this is taking place between August 6th (atomic bomb dropped on Hiroshima) and August 15th (surrender of Japan).
A key part of the plot is the the English class system and people "knowing their place" within it and the problems that arise when people do not follow this (for example the social conflict involved in the Lord Pym standing for election on behalf of the Conservative Party while the family butler [Cecil Parker] stands on behalf of the Labour Party). This theme is similar to that used in The Admirable Crichton, in which Cecil Parker plays Lord Loam and finds his social position reversed with regards his butler.