The British did not sail directly to Washington, DC—it is an inland city on the Potomac River, ~100 miles from the Chesapeake Bay.
During the War of 1812 (August 1814), the British expeditionary force:
The Potomac was navigable only to Georgetown (then a separate port); the British fleet ascended the Potomac to Alexandria, VA (surrendered without fight) but could not reach the capital due to shallow channels and Fort Washington (which they bypassed).
Washington was captured by land invasion from the Chesapeake, not by sailing to its doorstep.