The term, a Whitehall farce is derived from a variation of the comedy tradition of British farce that played the Whitehall theatre in London during the 1930's and 1940's.
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.
References edit
For a more extensive history of the British farce tradition see also:
[1] Theater: England's Endless Love Affair with Farce—NY Times, Aug 1987