Woodhouse was born at Clifton, Westmorland, England, the son of Richard Woodhouse, a station master, and his wife Mary, "née" Titterington. Educated at Sedbergh School, Yorkshire, Woodhouse won an open exhibition to Queen's College, Oxford, (B.A., 1889; M.A., 1895). He graduated with a first class in classical and a first class in the final school of "Literae Humaniores", was appointed a Newton student at the British School at Athens, and during 1890 travelled in Greece and directed the excavations at Megalopolis.