www.phrases.org.uk says:

It's a cliche from the movies - "Once around the park and home, James," said to the chauffeur. According to one reference, the original saying was: "Home, James, and don't spare the horses!" said to the coachman. Dates from 1870 if not earlier. There was a song by that title in 1934 that gave the phrase "a popular boost." (From Dictionary of Catch Phrases: American and British from the Sixteenth Century to the Present Day by Eric Partridge, updated and edited by Paul Beal, Scarborough House, Lanham, Md., 1992)