Penley was born at St Peters, Broadstairs, Kent, the only son of William George Robinson Penley (1823–1903), a schoolmaster, and his first wife, Emily Ann, "née" Wooton, the widow of Walter Pilcher. Although Penley's relatives included the painter Aaron Edwin Penley, his family was more generally associated with the theatre. His great-grandfather, William (1773–1838), a comedian at Drury Lane, was the first in a theatrical line that included Sampson (1792–1838) actor-manager at the Theatre Royal, Windsor, and Thomas Turpin Belville (1805–93), a theatre manager in Bath. Penley was educated at his father's schools – first at Grove House, St Peters, and then in London, where his father moved to a school in Westminster. He was a chorister at the Chapel Royal and at Westminster Abbey. After an apprenticeship with a City firm of milliners he joined the staff of Copestake, Moore, Crampton & Co, wholesale drapers and mercers. His obituarist in "The Times" speculated that Penley's career in retail may have been cut short by an irrepressible sense of humour ill-suited to a serious commercial concern.