In French, the phrase "filer à l'anglaise" (English leave) means the same thing.
The term is especially used to mean the act of leisurely absence from a military unit. This comes from the rich history of Franco-English conflict; as Spain has a similar saying concerning the French, it may have come from the Napoleonic campaign in the Iberic Peninsula which pitted the French against an Anglo-Portuguese & Spanish alliance. The phrase has a perfect French and Italian equivalent in filer à l'anglaise and filarsela all'inglese, literally, "to take the English leave".
The actual derivation may have its roots in American history during the French and Indian wars. About 140 French soldiers were captured near Lake George in New York and ferried to an island in the lake. The French, knowing the area better than the British, waited until near dawn and quietly waded ashore leaving their captors bewildered on arising. Though its role as such didn't last a day, the island has been named Prison Island.
In Treasure Island, by Robert Louis Stevenson, the main character, Jim, refers to taking "a French leave" when he leaves the shelter unbeknownst to the captain.
In the movie Mr. Smith Goes to Washington Senator Smith is accused of taking "French leave" when he fails to show up at his office in a timely manner upon first arriving in Washington, D.C.