1
general::
Very quickly, as in You'd better get here on the double. This expression, also put as at the double, came from the military, where it means "double time"? that is, marching twice as fast as normally. [Early 1800s]
American Heritage Idioms
2
general::
Phrase(s): on the double
very fast; twice as fast as normal. (Originally military. Alludes to "double time" in marching.) • Get over here right now—on the double! • She wants to see you in her office on the double.
McGrawhill's American Idioms And Phrasal Verbs