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Whitehall farces were typical of the farce tradition and followed the Aldwych farce which played at the Aldwych theater a decade earlier. The typical Whitehall plot derived its entertainment value from situations involving a chaotic and improbable series of accidents that caused drama and panic for the characters involved but amusement for the audience.
Whitehall farce became a moniker attached to any series of unlikely events that caused grief at the time to everyone involved but could—-perhaps only with distance or hindsight—-be considered ridiculous or amusing.
For a more extensive history of the British farce tradition see also:
 Theater: England's Endless Love Affair with Farce—NY Times, Aug 1987