The “boot” was originally a projection on each side of the coach, where the passengers sat with their backs to the carriage. Such a “boot” is seen in the carriage containing the attendants of Queen Elizabeth, in Hoefnagel’s well-known picture of Nonsuch Palace, dated 1582. Taylor, the Water Poet, the inveterate opponent of the introduction of coaches, thus satirizes the one in which he was forced to take his place as a passenger: “It wears two boots and no spurs, sometimes having two pairs of legs in one boot; and oftentimes against nature most preposterously it makes fair ladies wear the boot. Moreover, it makes people imitate sea-crabs, in being drawn sideways, as they are when they sit in the boot of the coach.” In course of time these projections were abolished, and the coach then consisted of three parts, viz., the body, the boot (on the top of which the coachman sat), and the baskets at the back.
This text comes from a footnote on a diary entry in the 1893 edition edited by Henry B. Wheatley.