Headlong; in reckless confusion. From the players of pallmall, who rush heedlessly to strike the ball. The “pall” is the ball (Italian, palla), and the “mall” is the mallet or bat (Italian, maglia; Latin, malleus). Sometimes the game is called “pall mall;” and sometimes the ground set apart for the game, as Pall Mall, Londo It is not quite certain that pell-mell is the same compound word as pall-mall.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894