For non-British audiences, "August Monday" is a bank holiday that marks the end of summer for students (much like Labor Day used to be in the United States). It was established in 1871 to give bankers a day to enjoy local cricket games, and was celebrated on the first Monday in August. In 1971 August Monday was moved to the last Monday of August in England, Wales, and Northern Ireland.
The poem that Siegfried quotes when talking about the cricket match to James is the first verse of Vitaï Lampada by Henry Newbolt.